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(cos(2x))*atan(x)
The derivative of the function/ (cos(2x))*atan(x)

Derivative of (cos(2x))*atan(x)

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
cos(2*x)*atan(x)
cos⁡(2x)atan⁡(x)\cos{\left(2 x \right)} \operatorname{atan}{\left(x \right)} 
d                   
--(cos(2*x)*atan(x))
dx
ddxcos⁡(2x)atan⁡(x)\frac{d}{d x} \cos{\left(2 x \right)} \operatorname{atan}{\left(x \right)}
Transform
The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
cos(2*x)                     
-------- - 2*atan(x)*sin(2*x)
      2                      
 1 + x
−2sin⁡(2x)atan⁡(x)+cos⁡(2x)x2+1- 2 \sin{\left(2 x \right)} \operatorname{atan}{\left(x \right)} + \frac{\cos{\left(2 x \right)}}{x^{2} + 1}
Simplify
The second derivative [src] 
   /2*sin(2*x)                        x*cos(2*x)\
-2*|---------- + 2*atan(x)*cos(2*x) + ----------|
   |       2                                  2 |
   |  1 + x                           /     2\  |
   \                                  \1 + x /  /
−2(xcos⁡(2x)(x2+1)2+2cos⁡(2x)atan⁡(x)+2sin⁡(2x)x2+1)- 2 \left(\frac{x \cos{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}} + 2 \cos{\left(2 x \right)} \operatorname{atan}{\left(x \right)} + \frac{2 \sin{\left(2 x \right)}}{x^{2} + 1}\right)
Simplify
The third derivative [src] 
  /                                    /         2 \                        \
  |                                    |      4*x  |                        |
  |                                    |-1 + ------|*cos(2*x)               |
  |                                    |          2|                        |
  |  6*cos(2*x)                        \     1 + x /            6*x*sin(2*x)|
2*|- ---------- + 4*atan(x)*sin(2*x) + ---------------------- + ------------|
  |         2                                        2                   2  |
  |    1 + x                                 /     2\            /     2\   |
  \                                          \1 + x /            \1 + x /   /
2⋅(6xsin⁡(2x)(x2+1)2+4sin⁡(2x)atan⁡(x)−6cos⁡(2x)x2+1+(4x2x2+1−1)cos⁡(2x)(x2+1)2)2 \cdot \left(\frac{6 x \sin{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}} + 4 \sin{\left(2 x \right)} \operatorname{atan}{\left(x \right)} - \frac{6 \cos{\left(2 x \right)}}{x^{2} + 1} + \frac{\left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \cos{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}}\right)
Simplify
The graph
Derivative of (cos(2x))*atan(x)
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