# What is the second derivative of #f(x)= ln (x^2+2)#?

##### 1 Answer

Feb 2, 2016

#### Explanation:

To find the first derivative, use the chain rule in conjunction with the knowledge that

#f'(x)=(d/dx[x^2+2])/(x^2+2)=(2x)/(x^2+2)#

To find the second derivative, use the quotient rule. This gives:

#f''(x)=((x^2+2)d/dx[2x]-2xd/dx[x^2+2])/(x^2+2)^2#

These derivatives can be found through the power rule.

#f''(x)=((x^2+2)(2)-2x(2x))/(x^2+2)^2#

#f''(x)=(2(2-x^2))/(x^2+2)^2#