Question

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

Answer 1

You can use the Chain Rule to get:
`f'(x)=1/(x^2+2)*2x=(2x)/(x^2+2)`

Then the Quotient Rule to get:

`f''(x)=(2(x^2+2)-2x*2x)/(x^2+2)^2=`
`=(2x^2+4-4x^2)/(x^2+2)^2=(4-2x^2)/(x^2+2)^2`