Производная acot(3*x)^(5)

Вы ввели

    5     
acot (3*x)

$$\operatorname{acot}^{5}{\left (3 x \right )}$$

Первая производная

        4     
-15*acot (3*x)
--------------
          2   
   1 + 9*x    

$$- \frac{15 \operatorname{acot}^{4}{\left (3 x \right )}}{9 x^{2} + 1}$$

Вторая производная

       3                         
90*acot (3*x)*(2 + 3*x*acot(3*x))
---------------------------------
                     2           
           /       2\            
           \1 + 9*x /            

$$\frac{90 \operatorname{acot}^{3}{\left (3 x \right )}}{\left(9 x^{2} + 1\right)^{2}} \left(3 x \operatorname{acot}{\left (3 x \right )} + 2\right)$$

Третья производная

               /                                             2     2     \
        2      |    2           6       36*x*acot(3*x)   36*x *acot (3*x)|
270*acot (3*x)*|acot (3*x) - -------- - -------------- - ----------------|
               |                    2             2                 2    |
               \             1 + 9*x       1 + 9*x           1 + 9*x     /
--------------------------------------------------------------------------
                                         2                                
                               /       2\                                 
                               \1 + 9*x /                                 

$$\frac{270 \operatorname{acot}^{2}{\left (3 x \right )}}{\left(9 x^{2} + 1\right)^{2}} \left(- \frac{36 x^{2} \operatorname{acot}^{2}{\left (3 x \right )}}{9 x^{2} + 1} - \frac{36 x \operatorname{acot}{\left (3 x \right )}}{9 x^{2} + 1} + \operatorname{acot}^{2}{\left (3 x \right )} - \frac{6}{9 x^{2} + 1}\right)$$