Производная cot(acot(x))

Вы ввели

cot(acot(x))

$$\cot{\left (\operatorname{acot}{\left (x \right )} \right )}$$

Первая производная

 /        2         \ 
-\-1 - cot (acot(x))/ 
----------------------
             2        
        1 + x         

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

Вторая производная

  /       2         \                    
2*\1 + cot (acot(x))/*(-x + cot(acot(x)))
-----------------------------------------
                        2                
                /     2\                 
                \1 + x /                 

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

Третья производная

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

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