Производная atan(tanh(x))

Вы ввели

atan(tanh(x))

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

Первая производная

        2   
1 - tanh (x)
------------
        2   
1 + tanh (x)

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

Вторая производная

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

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

Третья производная

                  /                                2                    2                                      \
                  |                 /         2   \      /         2   \      2            2    /         2   \|
  /         2   \ |          2      \-1 + tanh (x)/    4*\-1 + tanh (x)/ *tanh (x)   6*tanh (x)*\-1 + tanh (x)/|
2*\-1 + tanh (x)/*|1 - 3*tanh (x) + ---------------- - --------------------------- + --------------------------|
                  |                           2                            2                        2          |
                  |                   1 + tanh (x)           /        2   \                 1 + tanh (x)       |
                  \                                          \1 + tanh (x)/                                    /
----------------------------------------------------------------------------------------------------------------
                                                          2                                                     
                                                  1 + tanh (x)                                                  

$$\frac{2}{\tanh^{2}{\left (x \right )} + 1} \left(\tanh^{2}{\left (x \right )} - 1\right) \left(\frac{\left(\tanh^{2}{\left (x \right )} - 1\right)^{2}}{\tanh^{2}{\left (x \right )} + 1} - \frac{4 \left(\tanh^{2}{\left (x \right )} - 1\right)^{2} \tanh^{2}{\left (x \right )}}{\left(\tanh^{2}{\left (x \right )} + 1\right)^{2}} + \frac{6 \left(\tanh^{2}{\left (x \right )} - 1\right) \tanh^{2}{\left (x \right )}}{\tanh^{2}{\left (x \right )} + 1} - 3 \tanh^{2}{\left (x \right )} + 1\right)$$

График