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2^cosx×arcctg5x^3
The derivative of the function/ 2^cosx×arcctg5x^3

Derivative of 2^cosx×arcctg5x^3

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

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The solution

You have entered [src] 
 cos(x)     3     
2      *acot (5*x)
2cos⁡(x)acot⁡3(5x)2^{\cos{\left(x \right)}} \operatorname{acot}^{3}{\left(5 x \right)} 
d / cos(x)     3     \
--\2      *acot (5*x)/
dx
ddx2cos⁡(x)acot⁡3(5x)\frac{d}{d x} 2^{\cos{\left(x \right)}} \operatorname{acot}^{3}{\left(5 x \right)}
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The graph
02468-8-6-4-2-1010-5050
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The first derivative [src] 
      cos(x)     2                                        
  15*2      *acot (5*x)    cos(x)     3                   
- --------------------- - 2      *acot (5*x)*log(2)*sin(x)
                2                                         
        1 + 25*x
−2cos⁡(x)log⁡(2)sin⁡(x)acot⁡3(5x)−15⋅2cos⁡(x)acot⁡2(5x)25x2+1- 2^{\cos{\left(x \right)}} \log{\left(2 \right)} \sin{\left(x \right)} \operatorname{acot}^{3}{\left(5 x \right)} - \frac{15 \cdot 2^{\cos{\left(x \right)}} \operatorname{acot}^{2}{\left(5 x \right)}}{25 x^{2} + 1}
Simplify
The second derivative [src] 
 cos(x) /150*(1 + 5*x*acot(5*x))       2      /             2          \          30*acot(5*x)*log(2)*sin(x)\          
2      *|----------------------- + acot (5*x)*\-cos(x) + sin (x)*log(2)/*log(2) + --------------------------|*acot(5*x)
        |                 2                                                                       2         |          
        |      /        2\                                                                1 + 25*x          |          
        \      \1 + 25*x /                                                                                  /
2cos⁡(x)((log⁡(2)sin⁡2(x)−cos⁡(x))log⁡(2)acot⁡2(5x)+30log⁡(2)sin⁡(x)acot⁡(5x)25x2+1+150⋅(5xacot⁡(5x)+1)(25x2+1)2)acot⁡(5x)2^{\cos{\left(x \right)}} \left(\left(\log{\left(2 \right)} \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(2 \right)} \operatorname{acot}^{2}{\left(5 x \right)} + \frac{30 \log{\left(2 \right)} \sin{\left(x \right)} \operatorname{acot}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{150 \cdot \left(5 x \operatorname{acot}{\left(5 x \right)} + 1\right)}{\left(25 x^{2} + 1\right)^{2}}\right) \operatorname{acot}{\left(5 x \right)}
Simplify
The third derivative [src] 
        /      /                                               2     2     \                                                                                                                                                                       \
        |      |    1           2        30*x*acot(5*x)   100*x *acot (5*x)|                                                                                                                                                                       |
        |  750*|--------- - acot (5*x) + -------------- + -----------------|                                                                                                                                                                       |
        |      |        2                          2                  2    |                                                                             2      /             2          \                                                         |
 cos(x) |      \1 + 25*x                   1 + 25*x           1 + 25*x     /       3      /       2       2                     \                 45*acot (5*x)*\-cos(x) + sin (x)*log(2)/*log(2)   450*(1 + 5*x*acot(5*x))*acot(5*x)*log(2)*sin(x)|
2      *|- ----------------------------------------------------------------- + acot (5*x)*\1 - log (2)*sin (x) + 3*cos(x)*log(2)/*log(2)*sin(x) - ----------------------------------------------- - -----------------------------------------------|
        |                                        2                                                                                                                           2                                                   2                 |
        |                             /        2\                                                                                                                    1 + 25*x                                         /        2\                  |
        \                             \1 + 25*x /                                                                                                                                                                     \1 + 25*x /                  /
2cos⁡(x)((−log⁡(2)2sin⁡2(x)+3log⁡(2)cos⁡(x)+1)log⁡(2)sin⁡(x)acot⁡3(5x)−45(log⁡(2)sin⁡2(x)−cos⁡(x))log⁡(2)acot⁡2(5x)25x2+1−450⋅(5xacot⁡(5x)+1)log⁡(2)sin⁡(x)acot⁡(5x)(25x2+1)2−750⋅(100x2acot⁡2(5x)25x2+1+30xacot⁡(5x)25x2+1−acot⁡2(5x)+125x2+1)(25x2+1)2)2^{\cos{\left(x \right)}} \left(\left(- \log{\left(2 \right)}^{2} \sin^{2}{\left(x \right)} + 3 \log{\left(2 \right)} \cos{\left(x \right)} + 1\right) \log{\left(2 \right)} \sin{\left(x \right)} \operatorname{acot}^{3}{\left(5 x \right)} - \frac{45 \left(\log{\left(2 \right)} \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(2 \right)} \operatorname{acot}^{2}{\left(5 x \right)}}{25 x^{2} + 1} - \frac{450 \cdot \left(5 x \operatorname{acot}{\left(5 x \right)} + 1\right) \log{\left(2 \right)} \sin{\left(x \right)} \operatorname{acot}{\left(5 x \right)}}{\left(25 x^{2} + 1\right)^{2}} - \frac{750 \cdot \left(\frac{100 x^{2} \operatorname{acot}^{2}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{30 x \operatorname{acot}{\left(5 x \right)}}{25 x^{2} + 1} - \operatorname{acot}^{2}{\left(5 x \right)} + \frac{1}{25 x^{2} + 1}\right)}{\left(25 x^{2} + 1\right)^{2}}\right)
Simplify
The graph
Derivative of 2^cosx×arcctg5x^3
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