# What's the second derivative of #ln(f(x))#?

##### 1 Answer

Oct 12, 2016

#### Explanation:

#y=ln(f(x))#

Through the chain rule and the knowledge that

#dy/dx=1/f(x)*f'(x)=(f'(x))/f(x)#

To differentiate this again, we will use the quotient rule.

#(d^2y)/(dx^2)=(f(x)d/dxf'(x)-f'(x)d/dxf(x))/(f(x))^2#

#(d^2y)/(dx^2)=(f(x)f''(x)-(f'(x))^2)/(f(x))^2#