Производная sinh(x)^(2)/x

Вы ввели

    2   
sinh (x)
--------
   x    

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

  /        2            2            2                                           \
  |  3*cosh (x)   3*sinh (x)   3*sinh (x)                       6*cosh(x)*sinh(x)|
2*|- ---------- - ---------- - ---------- + 4*cosh(x)*sinh(x) + -----------------|
  |      x            x             3                                    2       |
  \                                x                                    x        /
----------------------------------------------------------------------------------
                                        x                                         

$$\frac{1}{x} \left(8 \sinh{\left (x \right )} \cosh{\left (x \right )} - \frac{6}{x} \sinh^{2}{\left (x \right )} - \frac{6}{x} \cosh^{2}{\left (x \right )} + \frac{12}{x^{2}} \sinh{\left (x \right )} \cosh{\left (x \right )} - \frac{6}{x^{3}} \sinh^{2}{\left (x \right )}\right)$$