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The derivative of the function/ arctg(x^2)-2*cos(2x)

Derivative of arctg(x^2)-2*cos(2x)

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

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The solution

You have entered [src] 
    / 2\             
atan\x / - 2*cos(2*x)
$$- 2 \cos{\left(2 x \right)} + \operatorname{atan}{\left(x^{2} \right)}$$ 
atan(x^2) - 2*cos(2*x)
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
              2*x  
4*sin(2*x) + ------
                  4
             1 + x
$$\frac{2 x}{x^{4} + 1} + 4 \sin{\left(2 x \right)}$$
Simplify
The second derivative [src] 
  /                            4  \
  |  1                      4*x   |
2*|------ + 4*cos(2*x) - ---------|
  |     4                        2|
  |1 + x                 /     4\ |
  \                      \1 + x / /
$$2 \left(- \frac{4 x^{4}}{\left(x^{4} + 1\right)^{2}} + 4 \cos{\left(2 x \right)} + \frac{1}{x^{4} + 1}\right)$$
Simplify
The third derivative [src] 
  /                    3           7  \
  |                 5*x         8*x   |
8*|-2*sin(2*x) - --------- + ---------|
  |                      2           3|
  |              /     4\    /     4\ |
  \              \1 + x /    \1 + x / /
$$8 \left(\frac{8 x^{7}}{\left(x^{4} + 1\right)^{3}} - \frac{5 x^{3}}{\left(x^{4} + 1\right)^{2}} - 2 \sin{\left(2 x \right)}\right)$$
Simplify
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