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2^cosx×arcctg5x^3

Derivative of 2^cosx×arcctg5x^3

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

The graph:

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The solution

You have entered [src]
 cos(x)     3     
2      *acot (5*x)
$$2^{\cos{\left(x \right)}} \operatorname{acot}^{3}{\left(5 x \right)}$$
d / cos(x)     3     \
--\2      *acot (5*x)/
dx                    
$$\frac{d}{d x} 2^{\cos{\left(x \right)}} \operatorname{acot}^{3}{\left(5 x \right)}$$
The graph
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                                          
$$- 2^{\cos{\left(x \right)}} \log{\left(2 \right)} \sin{\left(x \right)} \operatorname{acot}^{3}{\left(5 x \right)} - \frac{15 \cdot 2^{\cos{\left(x \right)}} \operatorname{acot}^{2}{\left(5 x \right)}}{25 x^{2} + 1}$$
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 /                                                                                  /          
$$2^{\cos{\left(x \right)}} \left(\left(\log{\left(2 \right)} \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(2 \right)} \operatorname{acot}^{2}{\left(5 x \right)} + \frac{30 \log{\left(2 \right)} \sin{\left(x \right)} \operatorname{acot}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{150 \cdot \left(5 x \operatorname{acot}{\left(5 x \right)} + 1\right)}{\left(25 x^{2} + 1\right)^{2}}\right) \operatorname{acot}{\left(5 x \right)}$$
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 /                  /
$$2^{\cos{\left(x \right)}} \left(\left(- \log{\left(2 \right)}^{2} \sin^{2}{\left(x \right)} + 3 \log{\left(2 \right)} \cos{\left(x \right)} + 1\right) \log{\left(2 \right)} \sin{\left(x \right)} \operatorname{acot}^{3}{\left(5 x \right)} - \frac{45 \left(\log{\left(2 \right)} \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(2 \right)} \operatorname{acot}^{2}{\left(5 x \right)}}{25 x^{2} + 1} - \frac{450 \cdot \left(5 x \operatorname{acot}{\left(5 x \right)} + 1\right) \log{\left(2 \right)} \sin{\left(x \right)} \operatorname{acot}{\left(5 x \right)}}{\left(25 x^{2} + 1\right)^{2}} - \frac{750 \cdot \left(\frac{100 x^{2} \operatorname{acot}^{2}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{30 x \operatorname{acot}{\left(5 x \right)}}{25 x^{2} + 1} - \operatorname{acot}^{2}{\left(5 x \right)} + \frac{1}{25 x^{2} + 1}\right)}{\left(25 x^{2} + 1\right)^{2}}\right)$$
The graph
Derivative of 2^cosx×arcctg5x^3