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The derivative of the function/ y=x^cosh(x)

Derivative of y=x^cosh(x)

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

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from to

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The solution

You have entered [src] 
 cosh(x)
x
xcosh⁡(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

    (log⁡(cosh⁡(x))+1)cosh⁡cosh⁡(x)(x)\left(\log{\left(\cosh{\left(x \right)} \right)} + 1\right) \cosh^{\cosh{\left(x \right)}}{\left(x \right)}

The answer is:

(log⁡(cosh⁡(x))+1)cosh⁡cosh⁡(x)(x)\left(\log{\left(\cosh{\left(x \right)} \right)} + 1\right) \cosh^{\cosh{\left(x \right)}}{\left(x \right)}

The first derivative [src] 
 cosh(x) /cosh(x)                 \
x       *|------- + log(x)*sinh(x)|
         \   x                    /
xcosh⁡(x)(log⁡(x)sinh⁡(x)+cosh⁡(x)x)x^{\cosh{\left(x \right)}} \left(\log{\left(x \right)} \sinh{\left(x \right)} + \frac{\cosh{\left(x \right)}}{x}\right)
Simplify
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               /
xcosh⁡(x)((log⁡(x)sinh⁡(x)+cosh⁡(x)x)2+log⁡(x)cosh⁡(x)+2sinh⁡(x)x−cosh⁡(x)x2)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)
Simplify
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               //
xcosh⁡(x)((log⁡(x)sinh⁡(x)+cosh⁡(x)x)3+3(log⁡(x)sinh⁡(x)+cosh⁡(x)x)(log⁡(x)cosh⁡(x)+2sinh⁡(x)x−cosh⁡(x)x2)+log⁡(x)sinh⁡(x)+3cosh⁡(x)x−3sinh⁡(x)x2+2cosh⁡(x)x3)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)
Simplify
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