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The derivative of the function/ ln(ch(x)^n)

Derivative of ln(ch(x)^n)

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] 
   /    n   \
log\cosh (x)/
$$\log{\left(\cosh^{n}{\left(x \right)} \right)}$$ 
log(cosh(x)^n)
The first derivative [src] 
n*sinh(x)
---------
 cosh(x)
$$\frac{n \sinh{\left(x \right)}}{\cosh{\left(x \right)}}$$
Simplify
The second derivative [src] 
  /        2   \
  |    sinh (x)|
n*|1 - --------|
  |        2   |
  \    cosh (x)/
$$n \left(- \frac{\sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} + 1\right)$$
Simplify
The third derivative [src] 
    /         2   \        
    |     sinh (x)|        
2*n*|-1 + --------|*sinh(x)
    |         2   |        
    \     cosh (x)/        
---------------------------
          cosh(x)
$$\frac{2 n \left(\frac{\sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} - 1\right) \sinh{\left(x \right)}}{\cosh{\left(x \right)}}$$
Simplify
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