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The derivative of the function/ arctg4x*cos5x

Derivative of arctg4x*cos5x

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

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The solution

You have entered [src] 
atan(4*x)*cos(5*x)
$$\cos{\left(5 x \right)} \operatorname{atan}{\left(4 x \right)}$$ 
atan(4*x)*cos(5*x)
The graph
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The first derivative [src] 
                        4*cos(5*x)
-5*atan(4*x)*sin(5*x) + ----------
                                2 
                        1 + 16*x
$$- 5 \sin{\left(5 x \right)} \operatorname{atan}{\left(4 x \right)} + \frac{4 \cos{\left(5 x \right)}}{16 x^{2} + 1}$$
Simplify
The second derivative [src] 
 /                        40*sin(5*x)   128*x*cos(5*x)\
-|25*atan(4*x)*cos(5*x) + ----------- + --------------|
 |                                 2                2 |
 |                         1 + 16*x      /        2\  |
 \                                       \1 + 16*x /  /
$$- (\frac{128 x \cos{\left(5 x \right)}}{\left(16 x^{2} + 1\right)^{2}} + 25 \cos{\left(5 x \right)} \operatorname{atan}{\left(4 x \right)} + \frac{40 \sin{\left(5 x \right)}}{16 x^{2} + 1})$$
Simplify
The third derivative [src] 
                                              /           2  \                           
                                              |       64*x   |                           
                                          128*|-1 + ---------|*cos(5*x)                  
                                              |             2|                           
  300*cos(5*x)                                \     1 + 16*x /            1920*x*sin(5*x)
- ------------ + 125*atan(4*x)*sin(5*x) + ----------------------------- + ---------------
           2                                                  2                        2 
   1 + 16*x                                        /        2\              /        2\  
                                                   \1 + 16*x /              \1 + 16*x /
$$\frac{1920 x \sin{\left(5 x \right)}}{\left(16 x^{2} + 1\right)^{2}} + 125 \sin{\left(5 x \right)} \operatorname{atan}{\left(4 x \right)} - \frac{300 \cos{\left(5 x \right)}}{16 x^{2} + 1} + \frac{128 \left(\frac{64 x^{2}}{16 x^{2} + 1} - 1\right) \cos{\left(5 x \right)}}{\left(16 x^{2} + 1\right)^{2}}$$
Simplify
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