Производная sqrt(atan(3*x)^(5))

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Решение

Вы ввели
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[text]
   ____________
  /     5      
\/  atan (3*x) 
$$\sqrt{\operatorname{atan}^{5}{\left (3 x \right )}}$$
График
Первая производная
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[text]
        ____________  
       /     5        
  15*\/  atan (3*x)   
----------------------
  /       2\          
2*\1 + 9*x /*atan(3*x)
$$\frac{15 \sqrt{\operatorname{atan}^{5}{\left (3 x \right )}}}{2 \left(9 x^{2} + 1\right) \operatorname{atan}{\left (3 x \right )}}$$
Вторая производная
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       ____________                   
      /     5       /          1     \
135*\/  atan (3*x) *|-x + -----------|
                    \     4*atan(3*x)/
--------------------------------------
                  2                   
        /       2\                    
        \1 + 9*x / *atan(3*x)         
$$\frac{135 \left(- x + \frac{1}{4 \operatorname{atan}{\left (3 x \right )}}\right) \sqrt{\operatorname{atan}^{5}{\left (3 x \right )}}}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left (3 x \right )}}$$
Третья производная
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       ____________ /          2                                                     \
      /     5       |      36*x                 3                       27*x         |
135*\/  atan (3*x) *|-1 + -------- + ----------------------- - ----------------------|
                    |            2     /       2\     2          /       2\          |
                    \     1 + 9*x    8*\1 + 9*x /*atan (3*x)   2*\1 + 9*x /*atan(3*x)/
--------------------------------------------------------------------------------------
                                          2                                           
                                /       2\                                            
                                \1 + 9*x / *atan(3*x)                                 
$$\frac{135 \sqrt{\operatorname{atan}^{5}{\left (3 x \right )}}}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left (3 x \right )}} \left(\frac{36 x^{2}}{9 x^{2} + 1} - \frac{27 x}{2 \left(9 x^{2} + 1\right) \operatorname{atan}{\left (3 x \right )}} - 1 + \frac{3}{8 \left(9 x^{2} + 1\right) \operatorname{atan}^{2}{\left (3 x \right )}}\right)$$