Производная atan(sinh(x))

Вы ввели

atan(sinh(x))

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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

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