Производная (arcctg^2)*5*x

Вы ввели

    2       
acot (x)*5*x

$$\operatorname{acot}^{2}{\left(x \right)} 5 x$$

d /    2       \
--\acot (x)*5*x/
dx              

$$\frac{d}{d x} \operatorname{acot}^{2}{\left(x \right)} 5 x$$

Первая производная

      2      10*x*acot(x)
5*acot (x) - ------------
                     2   
                1 + x    

$$- \frac{10 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + 5 \operatorname{acot}^{2}{\left(x \right)}$$

Вторая производная

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

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

Третья производная

   /        /                       2        \              \
   |        |            3*x     4*x *acot(x)|              |
10*|3 - 2*x*|-acot(x) + ------ + ------------| + 6*x*acot(x)|
   |        |                2           2   |              |
   \        \           1 + x       1 + x    /              /
-------------------------------------------------------------
                                  2                          
                          /     2\                           
                          \1 + x /                           

$$\frac{10 \left(- 2 x \left(\frac{4 x^{2} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} - \operatorname{acot}{\left(x \right)}\right) + 6 x \operatorname{acot}{\left(x \right)} + 3\right)}{\left(x^{2} + 1\right)^{2}}$$

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