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The derivative of the function/ arctgx+1/3(arctgx^3)

Derivative of arctgx+1/3(arctgx^3)

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

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The solution

You have entered [src] 
              3   
          acot (x)
acot(x) + --------
             3
$$\frac{\operatorname{acot}^{3}{\left(x \right)}}{3} + \operatorname{acot}{\left(x \right)}$$ 
acot(x) + acot(x)^3/3
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
               2   
    1      acot (x)
- ------ - --------
       2         2 
  1 + x     1 + x
$$- \frac{\operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{1}{x^{2} + 1}$$
Simplify
The second derivative [src] 
  /          2             \
2*\x + x*acot (x) + acot(x)/
----------------------------
                 2          
         /     2\           
         \1 + x /
$$\frac{2 \left(x \operatorname{acot}^{2}{\left(x \right)} + x + \operatorname{acot}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}}$$
Simplify
The third derivative [src] 
  /                            2                     2     2   \
  |        2        1       4*x     6*x*acot(x)   4*x *acot (x)|
2*|1 + acot (x) - ------ - ------ - ----------- - -------------|
  |                    2        2           2              2   |
  \               1 + x    1 + x       1 + x          1 + x    /
----------------------------------------------------------------
                                   2                            
                           /     2\                             
                           \1 + x /
$$\frac{2 \left(- \frac{4 x^{2} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{4 x^{2}}{x^{2} + 1} - \frac{6 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \operatorname{acot}^{2}{\left(x \right)} + 1 - \frac{1}{x^{2} + 1}\right)}{\left(x^{2} + 1\right)^{2}}$$
Simplify
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