Mister Exam

Derivative of y=ln*(ch(x))

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

The graph:

from to

Piecewise:

The solution

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