Question

What is the second derivative of `f(x)= ln (x^3+e^x)`?

Answer 1

`f''(x)=((x^3+e^x)(6x+e^x)-(3x^2+e^x)^2)/(x^3+e^x)^2`

Explanation:

We first use the log rule to find

`f'(x)=(3x^2+e^x)/(x^3+e^x)`

We now use the quotient rule to find

`f''(x)=((x^3+e^x)(6x+e^x)-(3x^2+e^x)(3x^2+e^x))/(x^3+e^x)^2`