Производная coth(x+1)^(2)

Вы ввели

    2       
coth (x + 1)

$$\coth^{2}{\left (x + 1 \right )}$$

Первая производная

-2*coth(x + 1)
--------------
     2        
 sinh (x + 1) 

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

Вторая производная

  /     1                                 \
2*|----------- + 2*cosh(1 + x)*coth(1 + x)|
  \sinh(1 + x)                            /
-------------------------------------------
                    3                      
                sinh (1 + x)               

$$\frac{1}{\sinh^{3}{\left (x + 1 \right )}} \left(4 \cosh{\left (x + 1 \right )} \coth{\left (x + 1 \right )} + \frac{2}{\sinh{\left (x + 1 \right )}}\right)$$

Третья производная

  /                        2                                 \
  |  3*cosh(1 + x)   3*cosh (1 + x)*coth(1 + x)              |
4*|- ------------- - -------------------------- + coth(1 + x)|
  |       3                     2                            |
  \   sinh (1 + x)          sinh (1 + x)                     /
--------------------------------------------------------------
                             2                                
                         sinh (1 + x)                         

$$\frac{1}{\sinh^{2}{\left (x + 1 \right )}} \left(4 \coth{\left (x + 1 \right )} - \frac{12 \cosh^{2}{\left (x + 1 \right )}}{\sinh^{2}{\left (x + 1 \right )}} \coth{\left (x + 1 \right )} - \frac{12 \cosh{\left (x + 1 \right )}}{\sinh^{3}{\left (x + 1 \right )}}\right)$$