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Derivative of arcctg(x)/(x^(1/3))

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

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The solution

You have entered [src]
acot(x)
-------
 3 ___ 
 \/ x  
$$\frac{\operatorname{acot}{\left(x \right)}}{\sqrt[3]{x}}$$
acot(x)/x^(1/3)
The graph
The first derivative [src]
        1          acot(x)
- -------------- - -------
  3 ___ /     2\       4/3
  \/ x *\1 + x /    3*x   
$$- \frac{1}{\sqrt[3]{x} \left(x^{2} + 1\right)} - \frac{\operatorname{acot}{\left(x \right)}}{3 x^{\frac{4}{3}}}$$
The second derivative [src]
  /    2/3                                \
  |   x               1          2*acot(x)|
2*|--------- + --------------- + ---------|
  |        2      4/3 /     2\        7/3 |
  |/     2\    3*x   *\1 + x /     9*x    |
  \\1 + x /                               /
$$2 \left(\frac{x^{\frac{2}{3}}}{\left(x^{2} + 1\right)^{2}} + \frac{1}{3 x^{\frac{4}{3}} \left(x^{2} + 1\right)} + \frac{2 \operatorname{acot}{\left(x \right)}}{9 x^{\frac{7}{3}}}\right)$$
The third derivative [src]
   /                     2                              \
   |                  4*x                               |
   |            -1 + ------                             |
   |                      2                             |
   |    1            1 + x          2         14*acot(x)|
-2*|--------- + ----------- + ------------- + ----------|
   |        2            2       2 /     2\         3   |
   |/     2\     /     2\     3*x *\1 + x /     27*x    |
   \\1 + x /     \1 + x /                               /
---------------------------------------------------------
                          3 ___                          
                          \/ x                           
$$- \frac{2 \left(\frac{\frac{4 x^{2}}{x^{2} + 1} - 1}{\left(x^{2} + 1\right)^{2}} + \frac{1}{\left(x^{2} + 1\right)^{2}} + \frac{2}{3 x^{2} \left(x^{2} + 1\right)} + \frac{14 \operatorname{acot}{\left(x \right)}}{27 x^{3}}\right)}{\sqrt[3]{x}}$$