Mister Exam

Derivative of y=x^cosh(x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 cosh(x)
x       
$$x^{\cosh{\left(x \right)}}$$
x^cosh(x)
Detail solution
  1. Don't know the steps in finding this derivative.

    But the derivative is


The answer is:

The first derivative [src]
 cosh(x) /cosh(x)                 \
x       *|------- + log(x)*sinh(x)|
         \   x                    /
$$x^{\cosh{\left(x \right)}} \left(\log{\left(x \right)} \sinh{\left(x \right)} + \frac{\cosh{\left(x \right)}}{x}\right)$$
The second derivative [src]
         /                          2                                       \
 cosh(x) |/cosh(x)                 \                     cosh(x)   2*sinh(x)|
x       *||------- + log(x)*sinh(x)|  + cosh(x)*log(x) - ------- + ---------|
         |\   x                    /                         2         x    |
         \                                                  x               /
$$x^{\cosh{\left(x \right)}} \left(\left(\log{\left(x \right)} \sinh{\left(x \right)} + \frac{\cosh{\left(x \right)}}{x}\right)^{2} + \log{\left(x \right)} \cosh{\left(x \right)} + \frac{2 \sinh{\left(x \right)}}{x} - \frac{\cosh{\left(x \right)}}{x^{2}}\right)$$
The third derivative [src]
         /                          3                                                                                                                           \
 cosh(x) |/cosh(x)                 \                     3*sinh(x)   2*cosh(x)   3*cosh(x)     /cosh(x)                 \ /                 cosh(x)   2*sinh(x)\|
x       *||------- + log(x)*sinh(x)|  + log(x)*sinh(x) - --------- + --------- + --------- + 3*|------- + log(x)*sinh(x)|*|cosh(x)*log(x) - ------- + ---------||
         |\   x                    /                          2           3          x         \   x                    / |                     2         x    ||
         \                                                   x           x                                                \                    x               //
$$x^{\cosh{\left(x \right)}} \left(\left(\log{\left(x \right)} \sinh{\left(x \right)} + \frac{\cosh{\left(x \right)}}{x}\right)^{3} + 3 \left(\log{\left(x \right)} \sinh{\left(x \right)} + \frac{\cosh{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \cosh{\left(x \right)} + \frac{2 \sinh{\left(x \right)}}{x} - \frac{\cosh{\left(x \right)}}{x^{2}}\right) + \log{\left(x \right)} \sinh{\left(x \right)} + \frac{3 \cosh{\left(x \right)}}{x} - \frac{3 \sinh{\left(x \right)}}{x^{2}} + \frac{2 \cosh{\left(x \right)}}{x^{3}}\right)$$