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The derivative of the function/ arctg(3x)/cos^3x+2x

Derivative of arctg(3x)/cos^3x+2x

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

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The solution

You have entered [src] 
atan(3*x)      
--------- + 2*x
    3          
 cos (x)
2x+atan⁡(3x)cos⁡3(x)2 x + \frac{\operatorname{atan}{\left(3 x \right)}}{\cos^{3}{\left(x \right)}} 
atan(3*x)/cos(x)^3 + 2*x
The graph
02468-8-6-4-2-1010-50000005000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
            3            3*atan(3*x)*sin(x)
2 + ------------------ + ------------------
    /       2\    3              4         
    \1 + 9*x /*cos (x)        cos (x)
3sin⁡(x)atan⁡(3x)cos⁡4(x)+2+3(9x2+1)cos⁡3(x)\frac{3 \sin{\left(x \right)} \operatorname{atan}{\left(3 x \right)}}{\cos^{4}{\left(x \right)}} + 2 + \frac{3}{\left(9 x^{2} + 1\right) \cos^{3}{\left(x \right)}}
Simplify
The second derivative [src] 
  /                     2                                             \
  |      18*x      4*sin (x)*atan(3*x)        6*sin(x)                |
3*|- ----------- + ------------------- + ----------------- + atan(3*x)|
  |            2            2            /       2\                   |
  |  /       2\          cos (x)         \1 + 9*x /*cos(x)            |
  \  \1 + 9*x /                                                       /
-----------------------------------------------------------------------
                                   3                                   
                                cos (x)
3(−18x(9x2+1)2+4sin⁡2(x)atan⁡(3x)cos⁡2(x)+atan⁡(3x)+6sin⁡(x)(9x2+1)cos⁡(x))cos⁡3(x)\frac{3 \left(- \frac{18 x}{\left(9 x^{2} + 1\right)^{2}} + \frac{4 \sin^{2}{\left(x \right)} \operatorname{atan}{\left(3 x \right)}}{\cos^{2}{\left(x \right)}} + \operatorname{atan}{\left(3 x \right)} + \frac{6 \sin{\left(x \right)}}{\left(9 x^{2} + 1\right) \cos{\left(x \right)}}\right)}{\cos^{3}{\left(x \right)}}
Simplify
The third derivative [src] 
  /                                   2                                 3                          2                            \
  |       18          9          648*x      11*atan(3*x)*sin(x)   20*sin (x)*atan(3*x)       36*sin (x)          162*x*sin(x)   |
3*|- ----------- + -------- + ----------- + ------------------- + -------------------- + ------------------ - ------------------|
  |            2          2             3          cos(x)                  3             /       2\    2                2       |
  |  /       2\    1 + 9*x    /       2\                                cos (x)          \1 + 9*x /*cos (x)   /       2\        |
  \  \1 + 9*x /               \1 + 9*x /                                                                      \1 + 9*x / *cos(x)/
---------------------------------------------------------------------------------------------------------------------------------
                                                                3                                                                
                                                             cos (x)
3(648x2(9x2+1)3−162xsin⁡(x)(9x2+1)2cos⁡(x)+20sin⁡3(x)atan⁡(3x)cos⁡3(x)+11sin⁡(x)atan⁡(3x)cos⁡(x)+36sin⁡2(x)(9x2+1)cos⁡2(x)+99x2+1−18(9x2+1)2)cos⁡3(x)\frac{3 \left(\frac{648 x^{2}}{\left(9 x^{2} + 1\right)^{3}} - \frac{162 x \sin{\left(x \right)}}{\left(9 x^{2} + 1\right)^{2} \cos{\left(x \right)}} + \frac{20 \sin^{3}{\left(x \right)} \operatorname{atan}{\left(3 x \right)}}{\cos^{3}{\left(x \right)}} + \frac{11 \sin{\left(x \right)} \operatorname{atan}{\left(3 x \right)}}{\cos{\left(x \right)}} + \frac{36 \sin^{2}{\left(x \right)}}{\left(9 x^{2} + 1\right) \cos^{2}{\left(x \right)}} + \frac{9}{9 x^{2} + 1} - \frac{18}{\left(9 x^{2} + 1\right)^{2}}\right)}{\cos^{3}{\left(x \right)}}
Simplify
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