Производная cosh(acot(x))

Вы ввели

cosh(acot(x))

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

Первая производная

-sinh(acot(x)) 
---------------
          2    
     1 + x     

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

Вторая производная

2*x*sinh(acot(x)) + cosh(acot(x))
---------------------------------
                    2            
            /     2\             
            \1 + x /             

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

Третья производная

                                     2                                  
                  sinh(acot(x))   8*x *sinh(acot(x))   6*x*cosh(acot(x))
2*sinh(acot(x)) - ------------- - ------------------ - -----------------
                           2                 2                    2     
                      1 + x             1 + x                1 + x      
------------------------------------------------------------------------
                                       2                                
                               /     2\                                 
                               \1 + x /                                 

$$\frac{1}{\left(x^{2} + 1\right)^{2}} \left(- \frac{8 x^{2}}{x^{2} + 1} \sinh{\left (\operatorname{acot}{\left (x \right )} \right )} - \frac{6 x}{x^{2} + 1} \cosh{\left (\operatorname{acot}{\left (x \right )} \right )} + 2 \sinh{\left (\operatorname{acot}{\left (x \right )} \right )} - \frac{1}{x^{2} + 1} \sinh{\left (\operatorname{acot}{\left (x \right )} \right )}\right)$$