Mister Exam

Other calculators

The derivative of the function/ x*sinx*cos2x

Derivative of x*sinx*cos2x

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
x*sin(x)*cos(2*x)
xsin⁡(x)cos⁡(2x)x \sin{\left(x \right)} \cos{\left(2 x \right)} 
(x*sin(x))*cos(2*x)
Detail solution

  1. Apply the product rule:

    ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}

    f(x)=xsin⁡(x)f{\left(x \right)} = x \sin{\left(x \right)}; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Apply the product rule:

      ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}

      f(x)=xf{\left(x \right)} = x; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

      1. Apply the power rule: xx goes to 11

      g(x)=sin⁡(x)g{\left(x \right)} = \sin{\left(x \right)}; to find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

      1. The derivative of sine is cosine:

        ddxsin⁡(x)=cos⁡(x)\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}

      The result is: xcos⁡(x)+sin⁡(x)x \cos{\left(x \right)} + \sin{\left(x \right)}

    g(x)=cos⁡(2x)g{\left(x \right)} = \cos{\left(2 x \right)}; to find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. Let u=2xu = 2 x.

    2. The derivative of cosine is negative sine:

      dducos⁡(u)=−sin⁡(u)\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}

    3. Then, apply the chain rule. Multiply by ddx2x\frac{d}{d x} 2 x:

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: xx goes to 11

        So, the result is: 22

      The result of the chain rule is:

      −2sin⁡(2x)- 2 \sin{\left(2 x \right)}

    The result is: −2xsin⁡(x)sin⁡(2x)+(xcos⁡(x)+sin⁡(x))cos⁡(2x)- 2 x \sin{\left(x \right)} \sin{\left(2 x \right)} + \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(2 x \right)}

  2. Now simplify:

    6xcos⁡3(x)−5xcos⁡(x)−2sin⁡3(x)+sin⁡(x)6 x \cos^{3}{\left(x \right)} - 5 x \cos{\left(x \right)} - 2 \sin^{3}{\left(x \right)} + \sin{\left(x \right)}

The answer is:

6xcos⁡3(x)−5xcos⁡(x)−2sin⁡3(x)+sin⁡(x)6 x \cos^{3}{\left(x \right)} - 5 x \cos{\left(x \right)} - 2 \sin^{3}{\left(x \right)} + \sin{\left(x \right)}

The graph
02468-8-6-4-2-1010-5050
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
(x*cos(x) + sin(x))*cos(2*x) - 2*x*sin(x)*sin(2*x)
−2xsin⁡(x)sin⁡(2x)+(xcos⁡(x)+sin⁡(x))cos⁡(2x)- 2 x \sin{\left(x \right)} \sin{\left(2 x \right)} + \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(2 x \right)}
Simplify
The second derivative [src] 
-((-2*cos(x) + x*sin(x))*cos(2*x) + 4*(x*cos(x) + sin(x))*sin(2*x) + 4*x*cos(2*x)*sin(x))
−(4xsin⁡(x)cos⁡(2x)+(xsin⁡(x)−2cos⁡(x))cos⁡(2x)+4(xcos⁡(x)+sin⁡(x))sin⁡(2x))- (4 x \sin{\left(x \right)} \cos{\left(2 x \right)} + \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 4 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \sin{\left(2 x \right)})
Simplify
The third derivative [src] 
-(3*sin(x) + x*cos(x))*cos(2*x) - 12*(x*cos(x) + sin(x))*cos(2*x) + 6*(-2*cos(x) + x*sin(x))*sin(2*x) + 8*x*sin(x)*sin(2*x)
8xsin⁡(x)sin⁡(2x)+6(xsin⁡(x)−2cos⁡(x))sin⁡(2x)−12(xcos⁡(x)+sin⁡(x))cos⁡(2x)−(xcos⁡(x)+3sin⁡(x))cos⁡(2x)8 x \sin{\left(x \right)} \sin{\left(2 x \right)} + 6 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \sin{\left(2 x \right)} - 12 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(2 x \right)} - \left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) \cos{\left(2 x \right)}
Simplify
100-я производная [src] 
(-100*cos(x) + x*sin(x))*cos(2*x) + 200*(99*sin(x) + x*cos(x))*sin(2*x) + 19800*(-98*cos(x) + x*sin(x))*cos(2*x) + 1293600*(97*sin(x) + x*cos(x))*sin(2*x) + 62739600*(-96*cos(x) + x*sin(x))*cos(2*x) + 2409200640*(95*sin(x) + x*cos(x))*sin(2*x) + 76291353600*(-94*cos(x) + x*sin(x))*cos(2*x) + 2048967782400*(93*sin(x) + x*cos(x))*sin(2*x) + 47638500940800*(-92*cos(x) + x*sin(x))*cos(2*x) + 973942685900800*(91*sin(x) + x*cos(x))*sin(2*x) + 17725756883394560*(-90*cos(x) + x*sin(x))*cos(2*x) + 290057839910092800*(89*sin(x) + x*cos(x))*sin(2*x) + 4302524625333043200*(-88*cos(x) + x*sin(x))*cos(2*x) + 58249564158355046400*(87*sin(x) + x*cos(x))*sin(2*x) + 723958868825269862400*(-86*cos(x) + x*sin(x))*cos(2*x) + 8301395029196427755520*(85*sin(x) + x*cos(x))*sin(2*x) + 88202322185212044902400*(-84*cos(x) + x*sin(x))*cos(2*x) + 871646478065624914329600*(83*sin(x) + x*cos(x))*sin(2*x) + 8038517519938540876595200*(-82*cos(x) + x*sin(x))*cos(2*x) + 69385098593153721250611200*(81*sin(x) + x*cos(x))*sin(2*x) + 562019298604545142129950720*(-80*cos(x) + x*sin(x))*cos(2*x) + 4282051798891772511466291200*(79*sin(x) + x*cos(x))*sin(2*x) + 30752917464768184400530636800*(-78*cos(x) + x*sin(x))*cos(2*x) + 208585005413210294194903449600*(77*sin(x) + x*cos(x))*sin(2*x) + 1338420451401432721083963801600*(-76*cos(x) + x*sin(x))*cos(2*x) + 8137596344520710944190499913728*(75*sin(x) + x*cos(x))*sin(2*x) + 46947671218388716985714422579200*(-74*cos(x) + x*sin(x))*cos(2*x) + 63382530011411470074835160268800*(x*cos(x) + sin(x))*sin(2*x) + 257342790382278893106879057100800*(73*sin(x) + x*cos(x))*sin(2*x) + 1341858835564739942628726512025600*(-72*cos(x) + x*sin(x))*cos(2*x) + 1568717617782433884352170216652800*(-2*cos(x) + x*sin(x))*cos(2*x) + 6663023183493881094432297163161600*(71*sin(x) + x*cos(x))*sin(2*x) + 25622387757113086777752113538662400*(3*sin(x) + x*cos(x))*sin(2*x) + 31538309735204370513646206572298240*(-70*cos(x) + x*sin(x))*cos(2*x) + 142431076223503608771305449036185600*(69*sin(x) + x*cos(x))*sin(2*x) + 310671451554996177180244376656281600*(-4*cos(x) + x*sin(x))*cos(2*x) + 614234016213859312826254748968550400*(-68*cos(x) + x*sin(x))*cos(2*x) + 2531388672881359592253655935143116800*(67*sin(x) + x*cos(x))*sin(2*x) + 2982445934927963300930346015900303360*(5*sin(x) + x*cos(x))*sin(2*x) + 9976649475473593687117349862034636800*(-66*cos(x) + x*sin(x))*cos(2*x) + 23611030318179709465698572625877401600*(-6*cos(x) + x*sin(x))*cos(2*x) + 37626220878928981905699719479673487360*(65*sin(x) + x*cos(x))*sin(2*x) + 135872464285021323548360098121043148800*(-64*cos(x) + x*sin(x))*cos(2*x) + 158531203564920906412547559059462553600*(7*sin(x) + x*cos(x))*sin(2*x) + 470045281850884578761894393499824947200*(63*sin(x) + x*cos(x))*sin(2*x) + 921462620721102768522932687033126092800*(-8*cos(x) + x*sin(x))*cos(2*x) + 1558571197716090971684176146867840614400*(-62*cos(x) + x*sin(x))*cos(2*x) + 4709697839241191928006100400391533363200*(9*sin(x) + x*cos(x))*sin(2*x) + 4955457141456289243303534415682365030400*(61*sin(x) + x*cos(x))*sin(2*x) + 15114144281441682192075779967831213342720*(-60*cos(x) + x*sin(x))*cos(2*x) + 21429125168547423272427756821781476802560*(-10*cos(x) + x*sin(x))*cos(2*x) + 44236519848121996659733990149749892710400*(59*sin(x) + x*cos(x))*sin(2*x) + 87664602962239458841749914270924223283200*(11*sin(x) + x*cos(x))*sin(2*x) + 124283555763771323948776448515963984281600*(-58*cos(x) + x*sin(x))*cos(2*x) + 325089569318304659871489265421343994675200*(-12*cos(x) + x*sin(x))*cos(2*x) + 335276569037150548326931814601205166899200*(57*sin(x) + x*cos(x))*sin(2*x) + 868671110687162784301596065103122477875200*(-56*cos(x) + x*sin(x))*cos(2*x) + 1100303157692723464180425206041471981977600*(13*sin(x) + x*cos(x))*sin(2*x) + 2162025875488049596483972428701104833822720*(55*sin(x) + x*cos(x))*sin(2*x) + 3418799097116676477989178318771716515430400*(-14*cos(x) + x*sin(x))*cos(2*x) + 5170061876167075122026890590372207211315200*(-54*cos(x) + x*sin(x))*cos(2*x) + 9800557411734472570235644513812254010900480*(15*sin(x) + x*cos(x))*sin(2*x) + 11880142183532853471891578377876561251532800*(53*sin(x) + x*cos(x))*sin(2*x) + 26032730624919692764688430739813799716454400*(-16*cos(x) + x*sin(x))*cos(2*x) + 26235313988635051417093902251144072763801600*(-52*cos(x) + x*sin(x))*cos(2*x) + 55683115404449905048525833349367011580313600*(51*sin(x) + x*cos(x))*sin(2*x) + 64316158014507476242171417121892916946534400*(17*sin(x) + x*cos(x))*sin(2*x) + 113593555425077806298992700032708703623839744*(-50*cos(x) + x*sin(x))*cos(2*x) + 148284475422336681336117433919919780737843200*(-18*cos(x) + x*sin(x))*cos(2*x) + 222732461617799620194103333397468046321254400*(49*sin(x) + x*cos(x))*sin(2*x) + 319982289069252838672674462669300579486924800*(19*sin(x) + x*cos(x))*sin(2*x) + 419765023818160822673502436018305164220825600*(-48*cos(x) + x*sin(x))*cos(2*x) + 647964135365236998312165786905333673461022720*(-20*cos(x) + x*sin(x))*cos(2*x) + 760329099746102622201061016184099920098099200*(47*sin(x) + x*cos(x))*sin(2*x) + 1234217400695689520594601498867302235163852800*(21*sin(x) + x*cos(x))*sin(2*x) + 1323535840298771231238883991135285046096691200*(-46*cos(x) + x*sin(x))*cos(2*x) + 2213914496499762786799587766989931349834465280*(45*sin(x) + x*cos(x))*sin(2*x) + 2215981242158169821067579963875383558589644800*(-22*cos(x) + x*sin(x))*cos(2*x) + 3558076869374618764499337482662389669376819200*(-44*cos(x) + x*sin(x))*cos(2*x) + 3757533410616027087897200808310432990652006400*(23*sin(x) + x*cos(x))*sin(2*x) + 5493171307104674583788450850426145454476492800*(43*sin(x) + x*cos(x))*sin(2*x) + 6027709846196543453501759629997986255837593600*(-24*cos(x) + x*sin(x))*cos(2*x) + 8145047110534517486307013329942215673878937600*(-42*cos(x) + x*sin(x))*cos(2*x) + 9162118966218746049322674637596939108873142272*(25*sin(x) + x*cos(x))*sin(2*x) + 11596338259066092692369307113816035874675097600*(41*sin(x) + x*cos(x))*sin(2*x) + 13214594662815499109600011496534046791643955200*(-26*cos(x) + x*sin(x))*cos(2*x) + 15848328954056993346238053055548582362055966720*(-40*cos(x) + x*sin(x))*cos(2*x) + 18108888982376795076118534273028138195956531200*(27*sin(x) + x*cos(x))*sin(2*x) + 20784693710238679798344987613834206376466841600*(39*sin(x) + x*cos(x))*sin(2*x) + 23606230280598322152797375034483108719729049600*(-28*cos(x) + x*sin(x))*cos(2*x) + 26148485635461564907595306998049485441361510400*(-38*cos(x) + x*sin(x))*cos(2*x) + 29304285865570330948300189697979031514146406400*(29*sin(x) + x*cos(x))*sin(2*x) + 31544204893572681475829259235742236405451980800*(37*sin(x) + x*cos(x))*sin(2*x) + 34676738274258224955488557809275187291739914240*(-30*cos(x) + x*sin(x))*cos(2*x) + 36472986908193412956427580991326960843803852800*(-36*cos(x) + x*sin(x))*cos(2*x) + 39151156116097995917487081397568759845512806400*(31*sin(x) + x*cos(x))*sin(2*x) + 40400847036768088197889012790392941242367344640*(35*sin(x) + x*cos(x))*sin(2*x) + 42209840187668151848540759631753819208443494400*(-32*cos(x) + x*sin(x))*cos(2*x) + 42849383220814638997761074171628877075238092800*(-34*cos(x) + x*sin(x))*cos(2*x) + 43488926253961126146981388711503934942032691200*(33*sin(x) + x*cos(x))*sin(2*x) + 1267650600228229401496703205376*x*cos(2*x)*sin(x)
1267650600228229401496703205376xsin⁡(x)cos⁡(2x)+(xsin⁡(x)−100cos⁡(x))cos⁡(2x)+19800(xsin⁡(x)−98cos⁡(x))cos⁡(2x)+62739600(xsin⁡(x)−96cos⁡(x))cos⁡(2x)+76291353600(xsin⁡(x)−94cos⁡(x))cos⁡(2x)+47638500940800(xsin⁡(x)−92cos⁡(x))cos⁡(2x)+17725756883394560(xsin⁡(x)−90cos⁡(x))cos⁡(2x)+4302524625333043200(xsin⁡(x)−88cos⁡(x))cos⁡(2x)+723958868825269862400(xsin⁡(x)−86cos⁡(x))cos⁡(2x)+88202322185212044902400(xsin⁡(x)−84cos⁡(x))cos⁡(2x)+8038517519938540876595200(xsin⁡(x)−82cos⁡(x))cos⁡(2x)+562019298604545142129950720(xsin⁡(x)−80cos⁡(x))cos⁡(2x)+30752917464768184400530636800(xsin⁡(x)−78cos⁡(x))cos⁡(2x)+1338420451401432721083963801600(xsin⁡(x)−76cos⁡(x))cos⁡(2x)+46947671218388716985714422579200(xsin⁡(x)−74cos⁡(x))cos⁡(2x)+1341858835564739942628726512025600(xsin⁡(x)−72cos⁡(x))cos⁡(2x)+31538309735204370513646206572298240(xsin⁡(x)−70cos⁡(x))cos⁡(2x)+614234016213859312826254748968550400(xsin⁡(x)−68cos⁡(x))cos⁡(2x)+9976649475473593687117349862034636800(xsin⁡(x)−66cos⁡(x))cos⁡(2x)+135872464285021323548360098121043148800(xsin⁡(x)−64cos⁡(x))cos⁡(2x)+1558571197716090971684176146867840614400(xsin⁡(x)−62cos⁡(x))cos⁡(2x)+15114144281441682192075779967831213342720(xsin⁡(x)−60cos⁡(x))cos⁡(2x)+124283555763771323948776448515963984281600(xsin⁡(x)−58cos⁡(x))cos⁡(2x)+868671110687162784301596065103122477875200(xsin⁡(x)−56cos⁡(x))cos⁡(2x)+5170061876167075122026890590372207211315200(xsin⁡(x)−54cos⁡(x))cos⁡(2x)+26235313988635051417093902251144072763801600(xsin⁡(x)−52cos⁡(x))cos⁡(2x)+113593555425077806298992700032708703623839744(xsin⁡(x)−50cos⁡(x))cos⁡(2x)+419765023818160822673502436018305164220825600(xsin⁡(x)−48cos⁡(x))cos⁡(2x)+1323535840298771231238883991135285046096691200(xsin⁡(x)−46cos⁡(x))cos⁡(2x)+3558076869374618764499337482662389669376819200(xsin⁡(x)−44cos⁡(x))cos⁡(2x)+8145047110534517486307013329942215673878937600(xsin⁡(x)−42cos⁡(x))cos⁡(2x)+15848328954056993346238053055548582362055966720(xsin⁡(x)−40cos⁡(x))cos⁡(2x)+26148485635461564907595306998049485441361510400(xsin⁡(x)−38cos⁡(x))cos⁡(2x)+36472986908193412956427580991326960843803852800(xsin⁡(x)−36cos⁡(x))cos⁡(2x)+42849383220814638997761074171628877075238092800(xsin⁡(x)−34cos⁡(x))cos⁡(2x)+42209840187668151848540759631753819208443494400(xsin⁡(x)−32cos⁡(x))cos⁡(2x)+34676738274258224955488557809275187291739914240(xsin⁡(x)−30cos⁡(x))cos⁡(2x)+23606230280598322152797375034483108719729049600(xsin⁡(x)−28cos⁡(x))cos⁡(2x)+13214594662815499109600011496534046791643955200(xsin⁡(x)−26cos⁡(x))cos⁡(2x)+6027709846196543453501759629997986255837593600(xsin⁡(x)−24cos⁡(x))cos⁡(2x)+2215981242158169821067579963875383558589644800(xsin⁡(x)−22cos⁡(x))cos⁡(2x)+647964135365236998312165786905333673461022720(xsin⁡(x)−20cos⁡(x))cos⁡(2x)+148284475422336681336117433919919780737843200(xsin⁡(x)−18cos⁡(x))cos⁡(2x)+26032730624919692764688430739813799716454400(xsin⁡(x)−16cos⁡(x))cos⁡(2x)+3418799097116676477989178318771716515430400(xsin⁡(x)−14cos⁡(x))cos⁡(2x)+325089569318304659871489265421343994675200(xsin⁡(x)−12cos⁡(x))cos⁡(2x)+21429125168547423272427756821781476802560(xsin⁡(x)−10cos⁡(x))cos⁡(2x)+921462620721102768522932687033126092800(xsin⁡(x)−8cos⁡(x))cos⁡(2x)+23611030318179709465698572625877401600(xsin⁡(x)−6cos⁡(x))cos⁡(2x)+310671451554996177180244376656281600(xsin⁡(x)−4cos⁡(x))cos⁡(2x)+1568717617782433884352170216652800(xsin⁡(x)−2cos⁡(x))cos⁡(2x)+63382530011411470074835160268800(xcos⁡(x)+sin⁡(x))sin⁡(2x)+25622387757113086777752113538662400(xcos⁡(x)+3sin⁡(x))sin⁡(2x)+2982445934927963300930346015900303360(xcos⁡(x)+5sin⁡(x))sin⁡(2x)+158531203564920906412547559059462553600(xcos⁡(x)+7sin⁡(x))sin⁡(2x)+4709697839241191928006100400391533363200(xcos⁡(x)+9sin⁡(x))sin⁡(2x)+87664602962239458841749914270924223283200(xcos⁡(x)+11sin⁡(x))sin⁡(2x)+1100303157692723464180425206041471981977600(xcos⁡(x)+13sin⁡(x))sin⁡(2x)+9800557411734472570235644513812254010900480(xcos⁡(x)+15sin⁡(x))sin⁡(2x)+64316158014507476242171417121892916946534400(xcos⁡(x)+17sin⁡(x))sin⁡(2x)+319982289069252838672674462669300579486924800(xcos⁡(x)+19sin⁡(x))sin⁡(2x)+1234217400695689520594601498867302235163852800(xcos⁡(x)+21sin⁡(x))sin⁡(2x)+3757533410616027087897200808310432990652006400(xcos⁡(x)+23sin⁡(x))sin⁡(2x)+9162118966218746049322674637596939108873142272(xcos⁡(x)+25sin⁡(x))sin⁡(2x)+18108888982376795076118534273028138195956531200(xcos⁡(x)+27sin⁡(x))sin⁡(2x)+29304285865570330948300189697979031514146406400(xcos⁡(x)+29sin⁡(x))sin⁡(2x)+39151156116097995917487081397568759845512806400(xcos⁡(x)+31sin⁡(x))sin⁡(2x)+43488926253961126146981388711503934942032691200(xcos⁡(x)+33sin⁡(x))sin⁡(2x)+40400847036768088197889012790392941242367344640(xcos⁡(x)+35sin⁡(x))sin⁡(2x)+31544204893572681475829259235742236405451980800(xcos⁡(x)+37sin⁡(x))sin⁡(2x)+20784693710238679798344987613834206376466841600(xcos⁡(x)+39sin⁡(x))sin⁡(2x)+11596338259066092692369307113816035874675097600(xcos⁡(x)+41sin⁡(x))sin⁡(2x)+5493171307104674583788450850426145454476492800(xcos⁡(x)+43sin⁡(x))sin⁡(2x)+2213914496499762786799587766989931349834465280(xcos⁡(x)+45sin⁡(x))sin⁡(2x)+760329099746102622201061016184099920098099200(xcos⁡(x)+47sin⁡(x))sin⁡(2x)+222732461617799620194103333397468046321254400(xcos⁡(x)+49sin⁡(x))sin⁡(2x)+55683115404449905048525833349367011580313600(xcos⁡(x)+51sin⁡(x))sin⁡(2x)+11880142183532853471891578377876561251532800(xcos⁡(x)+53sin⁡(x))sin⁡(2x)+2162025875488049596483972428701104833822720(xcos⁡(x)+55sin⁡(x))sin⁡(2x)+335276569037150548326931814601205166899200(xcos⁡(x)+57sin⁡(x))sin⁡(2x)+44236519848121996659733990149749892710400(xcos⁡(x)+59sin⁡(x))sin⁡(2x)+4955457141456289243303534415682365030400(xcos⁡(x)+61sin⁡(x))sin⁡(2x)+470045281850884578761894393499824947200(xcos⁡(x)+63sin⁡(x))sin⁡(2x)+37626220878928981905699719479673487360(xcos⁡(x)+65sin⁡(x))sin⁡(2x)+2531388672881359592253655935143116800(xcos⁡(x)+67sin⁡(x))sin⁡(2x)+142431076223503608771305449036185600(xcos⁡(x)+69sin⁡(x))sin⁡(2x)+6663023183493881094432297163161600(xcos⁡(x)+71sin⁡(x))sin⁡(2x)+257342790382278893106879057100800(xcos⁡(x)+73sin⁡(x))sin⁡(2x)+8137596344520710944190499913728(xcos⁡(x)+75sin⁡(x))sin⁡(2x)+208585005413210294194903449600(xcos⁡(x)+77sin⁡(x))sin⁡(2x)+4282051798891772511466291200(xcos⁡(x)+79sin⁡(x))sin⁡(2x)+69385098593153721250611200(xcos⁡(x)+81sin⁡(x))sin⁡(2x)+871646478065624914329600(xcos⁡(x)+83sin⁡(x))sin⁡(2x)+8301395029196427755520(xcos⁡(x)+85sin⁡(x))sin⁡(2x)+58249564158355046400(xcos⁡(x)+87sin⁡(x))sin⁡(2x)+290057839910092800(xcos⁡(x)+89sin⁡(x))sin⁡(2x)+973942685900800(xcos⁡(x)+91sin⁡(x))sin⁡(2x)+2048967782400(xcos⁡(x)+93sin⁡(x))sin⁡(2x)+2409200640(xcos⁡(x)+95sin⁡(x))sin⁡(2x)+1293600(xcos⁡(x)+97sin⁡(x))sin⁡(2x)+200(xcos⁡(x)+99sin⁡(x))sin⁡(2x)1267650600228229401496703205376 x \sin{\left(x \right)} \cos{\left(2 x \right)} + \left(x \sin{\left(x \right)} - 100 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 19800 \left(x \sin{\left(x \right)} - 98 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 62739600 \left(x \sin{\left(x \right)} - 96 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 76291353600 \left(x \sin{\left(x \right)} - 94 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 47638500940800 \left(x \sin{\left(x \right)} - 92 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 17725756883394560 \left(x \sin{\left(x \right)} - 90 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 4302524625333043200 \left(x \sin{\left(x \right)} - 88 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 723958868825269862400 \left(x \sin{\left(x \right)} - 86 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 88202322185212044902400 \left(x \sin{\left(x \right)} - 84 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 8038517519938540876595200 \left(x \sin{\left(x \right)} - 82 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 562019298604545142129950720 \left(x \sin{\left(x \right)} - 80 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 30752917464768184400530636800 \left(x \sin{\left(x \right)} - 78 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 1338420451401432721083963801600 \left(x \sin{\left(x \right)} - 76 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 46947671218388716985714422579200 \left(x \sin{\left(x \right)} - 74 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 1341858835564739942628726512025600 \left(x \sin{\left(x \right)} - 72 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 31538309735204370513646206572298240 \left(x \sin{\left(x \right)} - 70 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 614234016213859312826254748968550400 \left(x \sin{\left(x \right)} - 68 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 9976649475473593687117349862034636800 \left(x \sin{\left(x \right)} - 66 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 135872464285021323548360098121043148800 \left(x \sin{\left(x \right)} - 64 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 1558571197716090971684176146867840614400 \left(x \sin{\left(x \right)} - 62 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 15114144281441682192075779967831213342720 \left(x \sin{\left(x \right)} - 60 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 124283555763771323948776448515963984281600 \left(x \sin{\left(x \right)} - 58 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 868671110687162784301596065103122477875200 \left(x \sin{\left(x \right)} - 56 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 5170061876167075122026890590372207211315200 \left(x \sin{\left(x \right)} - 54 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 26235313988635051417093902251144072763801600 \left(x \sin{\left(x \right)} - 52 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 113593555425077806298992700032708703623839744 \left(x \sin{\left(x \right)} - 50 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 419765023818160822673502436018305164220825600 \left(x \sin{\left(x \right)} - 48 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 1323535840298771231238883991135285046096691200 \left(x \sin{\left(x \right)} - 46 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 3558076869374618764499337482662389669376819200 \left(x \sin{\left(x \right)} - 44 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 8145047110534517486307013329942215673878937600 \left(x \sin{\left(x \right)} - 42 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 15848328954056993346238053055548582362055966720 \left(x \sin{\left(x \right)} - 40 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 26148485635461564907595306998049485441361510400 \left(x \sin{\left(x \right)} - 38 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 36472986908193412956427580991326960843803852800 \left(x \sin{\left(x \right)} - 36 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 42849383220814638997761074171628877075238092800 \left(x \sin{\left(x \right)} - 34 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 42209840187668151848540759631753819208443494400 \left(x \sin{\left(x \right)} - 32 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 34676738274258224955488557809275187291739914240 \left(x \sin{\left(x \right)} - 30 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 23606230280598322152797375034483108719729049600 \left(x \sin{\left(x \right)} - 28 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 13214594662815499109600011496534046791643955200 \left(x \sin{\left(x \right)} - 26 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 6027709846196543453501759629997986255837593600 \left(x \sin{\left(x \right)} - 24 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 2215981242158169821067579963875383558589644800 \left(x \sin{\left(x \right)} - 22 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 647964135365236998312165786905333673461022720 \left(x \sin{\left(x \right)} - 20 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 148284475422336681336117433919919780737843200 \left(x \sin{\left(x \right)} - 18 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 26032730624919692764688430739813799716454400 \left(x \sin{\left(x \right)} - 16 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 3418799097116676477989178318771716515430400 \left(x \sin{\left(x \right)} - 14 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 325089569318304659871489265421343994675200 \left(x \sin{\left(x \right)} - 12 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 21429125168547423272427756821781476802560 \left(x \sin{\left(x \right)} - 10 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 921462620721102768522932687033126092800 \left(x \sin{\left(x \right)} - 8 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 23611030318179709465698572625877401600 \left(x \sin{\left(x \right)} - 6 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 310671451554996177180244376656281600 \left(x \sin{\left(x \right)} - 4 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 1568717617782433884352170216652800 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \cos{\left(2 x \right)} + 63382530011411470074835160268800 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 25622387757113086777752113538662400 \left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 2982445934927963300930346015900303360 \left(x \cos{\left(x \right)} + 5 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 158531203564920906412547559059462553600 \left(x \cos{\left(x \right)} + 7 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 4709697839241191928006100400391533363200 \left(x \cos{\left(x \right)} + 9 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 87664602962239458841749914270924223283200 \left(x \cos{\left(x \right)} + 11 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 1100303157692723464180425206041471981977600 \left(x \cos{\left(x \right)} + 13 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 9800557411734472570235644513812254010900480 \left(x \cos{\left(x \right)} + 15 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 64316158014507476242171417121892916946534400 \left(x \cos{\left(x \right)} + 17 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 319982289069252838672674462669300579486924800 \left(x \cos{\left(x \right)} + 19 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 1234217400695689520594601498867302235163852800 \left(x \cos{\left(x \right)} + 21 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 3757533410616027087897200808310432990652006400 \left(x \cos{\left(x \right)} + 23 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 9162118966218746049322674637596939108873142272 \left(x \cos{\left(x \right)} + 25 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 18108888982376795076118534273028138195956531200 \left(x \cos{\left(x \right)} + 27 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 29304285865570330948300189697979031514146406400 \left(x \cos{\left(x \right)} + 29 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 39151156116097995917487081397568759845512806400 \left(x \cos{\left(x \right)} + 31 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 43488926253961126146981388711503934942032691200 \left(x \cos{\left(x \right)} + 33 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 40400847036768088197889012790392941242367344640 \left(x \cos{\left(x \right)} + 35 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 31544204893572681475829259235742236405451980800 \left(x \cos{\left(x \right)} + 37 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 20784693710238679798344987613834206376466841600 \left(x \cos{\left(x \right)} + 39 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 11596338259066092692369307113816035874675097600 \left(x \cos{\left(x \right)} + 41 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 5493171307104674583788450850426145454476492800 \left(x \cos{\left(x \right)} + 43 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 2213914496499762786799587766989931349834465280 \left(x \cos{\left(x \right)} + 45 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 760329099746102622201061016184099920098099200 \left(x \cos{\left(x \right)} + 47 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 222732461617799620194103333397468046321254400 \left(x \cos{\left(x \right)} + 49 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 55683115404449905048525833349367011580313600 \left(x \cos{\left(x \right)} + 51 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 11880142183532853471891578377876561251532800 \left(x \cos{\left(x \right)} + 53 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 2162025875488049596483972428701104833822720 \left(x \cos{\left(x \right)} + 55 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 335276569037150548326931814601205166899200 \left(x \cos{\left(x \right)} + 57 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 44236519848121996659733990149749892710400 \left(x \cos{\left(x \right)} + 59 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 4955457141456289243303534415682365030400 \left(x \cos{\left(x \right)} + 61 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 470045281850884578761894393499824947200 \left(x \cos{\left(x \right)} + 63 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 37626220878928981905699719479673487360 \left(x \cos{\left(x \right)} + 65 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 2531388672881359592253655935143116800 \left(x \cos{\left(x \right)} + 67 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 142431076223503608771305449036185600 \left(x \cos{\left(x \right)} + 69 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 6663023183493881094432297163161600 \left(x \cos{\left(x \right)} + 71 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 257342790382278893106879057100800 \left(x \cos{\left(x \right)} + 73 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 8137596344520710944190499913728 \left(x \cos{\left(x \right)} + 75 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 208585005413210294194903449600 \left(x \cos{\left(x \right)} + 77 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 4282051798891772511466291200 \left(x \cos{\left(x \right)} + 79 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 69385098593153721250611200 \left(x \cos{\left(x \right)} + 81 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 871646478065624914329600 \left(x \cos{\left(x \right)} + 83 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 8301395029196427755520 \left(x \cos{\left(x \right)} + 85 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 58249564158355046400 \left(x \cos{\left(x \right)} + 87 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 290057839910092800 \left(x \cos{\left(x \right)} + 89 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 973942685900800 \left(x \cos{\left(x \right)} + 91 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 2048967782400 \left(x \cos{\left(x \right)} + 93 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 2409200640 \left(x \cos{\left(x \right)} + 95 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 1293600 \left(x \cos{\left(x \right)} + 97 \sin{\left(x \right)}\right) \sin{\left(2 x \right)} + 200 \left(x \cos{\left(x \right)} + 99 \sin{\left(x \right)}\right) \sin{\left(2 x \right)}
Simplify
    © Mister Exam – Calculator