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Derivative of (arctg(3x)^9)/9

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
    9     
atan (3*x)
----------
    9     
$$\frac{\operatorname{atan}^{9}{\left(3 x \right)}}{9}$$
atan(3*x)^9/9
The graph
The first derivative [src]
      8     
3*atan (3*x)
------------
         2  
  1 + 9*x   
$$\frac{3 \operatorname{atan}^{8}{\left(3 x \right)}}{9 x^{2} + 1}$$
The second derivative [src]
        7                          
-18*atan (3*x)*(-4 + 3*x*atan(3*x))
-----------------------------------
                      2            
            /       2\             
            \1 + 9*x /             
$$- \frac{18 \left(3 x \operatorname{atan}{\left(3 x \right)} - 4\right) \operatorname{atan}^{7}{\left(3 x \right)}}{\left(9 x^{2} + 1\right)^{2}}$$
The third derivative [src]
              /                                               2     2     \
       6      |      2           28      72*x*atan(3*x)   36*x *atan (3*x)|
54*atan (3*x)*|- atan (3*x) + -------- - -------------- + ----------------|
              |                      2             2                 2    |
              \               1 + 9*x       1 + 9*x           1 + 9*x     /
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                                          2                                
                                /       2\                                 
                                \1 + 9*x /                                 
$$\frac{54 \left(\frac{36 x^{2} \operatorname{atan}^{2}{\left(3 x \right)}}{9 x^{2} + 1} - \frac{72 x \operatorname{atan}{\left(3 x \right)}}{9 x^{2} + 1} - \operatorname{atan}^{2}{\left(3 x \right)} + \frac{28}{9 x^{2} + 1}\right) \operatorname{atan}^{6}{\left(3 x \right)}}{\left(9 x^{2} + 1\right)^{2}}$$