Производная tanh(sqrt(x))

Вы ввели

    /  ___\
tanh\\/ x /

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

Первая производная

        2/  ___\
1 - tanh \\/ x /
----------------
        ___     
    2*\/ x      

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

Вторая производная

                    /             /  ___\\
/         2/  ___\\ | 1     2*tanh\\/ x /|
\-1 + tanh \\/ x //*|---- + -------------|
                    | 3/2         x      |
                    \x                   /
------------------------------------------
                    4                     

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

Третья производная

                     /         /         2/  ___\\         2/  ___\         /  ___\\ 
 /         2/  ___\\ | 3     2*\-1 + tanh \\/ x //   4*tanh \\/ x /   6*tanh\\/ x /| 
-\-1 + tanh \\/ x //*|---- + --------------------- + -------------- + -------------| 
                     | 5/2             3/2                 3/2               2     | 
                     \x               x                   x                 x      / 
-------------------------------------------------------------------------------------
                                          8                                          

$$- \frac{1}{8} \left(\tanh^{2}{\left (\sqrt{x} \right )} - 1\right) \left(\frac{6}{x^{2}} \tanh{\left (\sqrt{x} \right )} + \frac{1}{x^{\frac{3}{2}}} \left(2 \tanh^{2}{\left (\sqrt{x} \right )} - 2\right) + \frac{4}{x^{\frac{3}{2}}} \tanh^{2}{\left (\sqrt{x} \right )} + \frac{3}{x^{\frac{5}{2}}}\right)$$