Производная tanh(x)^(1/2)

Вы ввели

  _________
\/ tanh(x) 

$$\sqrt{\tanh{\left (x \right )}}$$

Первая производная

        2   
1   tanh (x)
- - --------
2      2    
------------
  _________ 
\/ tanh(x)  

$$\frac{- \frac{1}{2} \tanh^{2}{\left (x \right )} + \frac{1}{2}}{\sqrt{\tanh{\left (x \right )}}}$$

Вторая производная

/          2   \ /                         2   \
|  1   tanh (x)| |    _________   -1 + tanh (x)|
|- - + --------|*|4*\/ tanh(x)  - -------------|
\  4      4    / |                      3/2    |
                 \                  tanh   (x) /

$$\left(- \frac{\tanh^{2}{\left (x \right )} - 1}{\tanh^{\frac{3}{2}}{\left (x \right )}} + 4 \sqrt{\tanh{\left (x \right )}}\right) \left(\frac{1}{4} \tanh^{2}{\left (x \right )} - \frac{1}{4}\right)$$

Третья производная

                 /                                   2                    \
/          2   \ |                    /         2   \      /         2   \|
|  1   tanh (x)| |         3/2      3*\-1 + tanh (x)/    4*\-1 + tanh (x)/|
|- - + --------|*|- 16*tanh   (x) - ------------------ + -----------------|
\  8      8    / |                          5/2               _________   |
                 \                      tanh   (x)          \/ tanh(x)    /

$$\left(\frac{1}{8} \tanh^{2}{\left (x \right )} - \frac{1}{8}\right) \left(- \frac{3 \left(\tanh^{2}{\left (x \right )} - 1\right)^{2}}{\tanh^{\frac{5}{2}}{\left (x \right )}} + \frac{4 \tanh^{2}{\left (x \right )} - 4}{\sqrt{\tanh{\left (x \right )}}} - 16 \tanh^{\frac{3}{2}}{\left (x \right )}\right)$$