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The derivative of the function/ arctg^3(x)+cos(9x)

Derivative of arctg^3(x)+cos(9x)

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

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The solution

You have entered [src] 
    3              
atan (x) + cos(9*x)
$$\cos{\left(9 x \right)} + \operatorname{atan}^{3}{\left(x \right)}$$ 
atan(x)^3 + cos(9*x)
The graph
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The first derivative [src] 
                    2   
              3*atan (x)
-9*sin(9*x) + ----------
                     2  
                1 + x
$$- 9 \sin{\left(9 x \right)} + \frac{3 \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1}$$
Simplify
The second derivative [src] 
  /                                   2   \
  |               2*atan(x)   2*x*atan (x)|
3*|-27*cos(9*x) + --------- - ------------|
  |                       2            2  |
  |               /     2\     /     2\   |
  \               \1 + x /     \1 + x /   /
$$3 \left(- \frac{2 x \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - 27 \cos{\left(9 x \right)} + \frac{2 \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right)$$
Simplify
The third derivative [src] 
  /                                 2                        2     2   \
  |    2                      2*atan (x)   12*x*atan(x)   8*x *atan (x)|
3*|--------- + 243*sin(9*x) - ---------- - ------------ + -------------|
  |        3                          2             3               3  |
  |/     2\                   /     2\      /     2\        /     2\   |
  \\1 + x /                   \1 + x /      \1 + x /        \1 + x /   /
$$3 \left(\frac{8 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{12 x \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} + 243 \sin{\left(9 x \right)} - \frac{2 \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{2}{\left(x^{2} + 1\right)^{3}}\right)$$
Simplify
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