Производная cosh(x)*atan(x)

Вы ввели

cosh(x)*atan(x)

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

Первая производная

cosh(x)                  
------- + atan(x)*sinh(x)
      2                  
 1 + x                   

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

Вторая производная

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

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

Третья производная

                                                           2        
                  2*cosh(x)   3*cosh(x)   6*x*sinh(x)   8*x *cosh(x)
atan(x)*sinh(x) - --------- + --------- - ----------- + ------------
                          2          2             2             3  
                  /     2\      1 + x      /     2\      /     2\   
                  \1 + x /                 \1 + x /      \1 + x /   

$$\frac{8 x^{2} \cosh{\left (x \right )}}{\left(x^{2} + 1\right)^{3}} - \frac{6 x \sinh{\left (x \right )}}{\left(x^{2} + 1\right)^{2}} + \sinh{\left (x \right )} \operatorname{atan}{\left (x \right )} + \frac{3 \cosh{\left (x \right )}}{x^{2} + 1} - \frac{2 \cosh{\left (x \right )}}{\left(x^{2} + 1\right)^{2}}$$