Производная arcctg^5

Вы ввели

    5   
acot (x)

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

d /    5   \
--\acot (x)/
dx          

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

Первая производная

       4   
-5*acot (x)
-----------
        2  
   1 + x   

$$- \frac{5 \operatorname{acot}^{4}{\left(x \right)}}{x^{2} + 1}$$

Вторая производная

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

$$\frac{10 \left(x \operatorname{acot}{\left(x \right)} + 2\right) \operatorname{acot}^{3}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}$$

Третья производная

            /                                      2     2   \
       2    |    2        6      12*x*acot(x)   4*x *acot (x)|
10*acot (x)*|acot (x) - ------ - ------------ - -------------|
            |                2           2               2   |
            \           1 + x       1 + x           1 + x    /
--------------------------------------------------------------
                                  2                           
                          /     2\                            
                          \1 + x /                            

$$\frac{10 \left(- \frac{4 x^{2} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{12 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \operatorname{acot}^{2}{\left(x \right)} - \frac{6}{x^{2} + 1}\right) \operatorname{acot}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}$$

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