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The derivative of the function/ 3^cos(x)*artan4x

Derivative of 3^cos(x)*artan4x

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

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The solution

You have entered [src] 
 cos(x)          
3      *atan(4*x)
3cos⁡(x)atan⁡(4x)3^{\cos{\left(x \right)}} \operatorname{atan}{\left(4 x \right)} 
3^cos(x)*atan(4*x)
The graph
02468-8-6-4-2-1010-2020
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   cos(x)                                  
4*3          cos(x)                        
--------- - 3      *atan(4*x)*log(3)*sin(x)
        2                                  
1 + 16*x
−3cos⁡(x)log⁡(3)sin⁡(x)atan⁡(4x)+4⋅3cos⁡(x)16x2+1- 3^{\cos{\left(x \right)}} \log{\left(3 \right)} \sin{\left(x \right)} \operatorname{atan}{\left(4 x \right)} + \frac{4 \cdot 3^{\cos{\left(x \right)}}}{16 x^{2} + 1}
Simplify
The second derivative [src] 
 cos(x) /     128*x       /             2          \                    8*log(3)*sin(x)\
3      *|- ------------ + \-cos(x) + sin (x)*log(3)/*atan(4*x)*log(3) - ---------------|
        |             2                                                            2   |
        |  /        2\                                                     1 + 16*x    |
        \  \1 + 16*x /                                                                 /
3cos⁡(x)(−128x(16x2+1)2+(log⁡(3)sin⁡2(x)−cos⁡(x))log⁡(3)atan⁡(4x)−8log⁡(3)sin⁡(x)16x2+1)3^{\cos{\left(x \right)}} \left(- \frac{128 x}{\left(16 x^{2} + 1\right)^{2}} + \left(\log{\left(3 \right)} \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(3 \right)} \operatorname{atan}{\left(4 x \right)} - \frac{8 \log{\left(3 \right)} \sin{\left(x \right)}}{16 x^{2} + 1}\right)
Simplify
The third derivative [src] 
        /    /           2  \                                                                                                                               \
        |    |       64*x   |                                                                                                                               |
        |128*|-1 + ---------|                                                                                                                               |
        |    |             2|      /             2          \                                                                                               |
 cos(x) |    \     1 + 16*x /   12*\-cos(x) + sin (x)*log(3)/*log(3)   /       2       2                     \                           384*x*log(3)*sin(x)|
3      *|-------------------- + ------------------------------------ + \1 - log (3)*sin (x) + 3*cos(x)*log(3)/*atan(4*x)*log(3)*sin(x) + -------------------|
        |               2                            2                                                                                                  2   |
        |    /        2\                     1 + 16*x                                                                                        /        2\    |
        \    \1 + 16*x /                                                                                                                     \1 + 16*x /    /
3cos⁡(x)(384xlog⁡(3)sin⁡(x)(16x2+1)2+(−log⁡(3)2sin⁡2(x)+3log⁡(3)cos⁡(x)+1)log⁡(3)sin⁡(x)atan⁡(4x)+12(log⁡(3)sin⁡2(x)−cos⁡(x))log⁡(3)16x2+1+128(64x216x2+1−1)(16x2+1)2)3^{\cos{\left(x \right)}} \left(\frac{384 x \log{\left(3 \right)} \sin{\left(x \right)}}{\left(16 x^{2} + 1\right)^{2}} + \left(- \log{\left(3 \right)}^{2} \sin^{2}{\left(x \right)} + 3 \log{\left(3 \right)} \cos{\left(x \right)} + 1\right) \log{\left(3 \right)} \sin{\left(x \right)} \operatorname{atan}{\left(4 x \right)} + \frac{12 \left(\log{\left(3 \right)} \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(3 \right)}}{16 x^{2} + 1} + \frac{128 \left(\frac{64 x^{2}}{16 x^{2} + 1} - 1\right)}{\left(16 x^{2} + 1\right)^{2}}\right)
Simplify
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