Chain rule problem: given $f(x)=\sqrt{4x+7}$ and $g(x)=e^{x+4}$, compute $f(g(x))'$. Question:
Given the functions $f(x)=\sqrt{4x+7}$ and $g(x)=e^{x+4}$, compute $f(g(x))'$.
My Approach:
I have found that found that $f(g(x))=\sqrt{4e^{x+4}+7}$. Should I now just differentiate it to get my answer or is there any simpler method to solve this problem. Any helpful suggestions or answers.

$f(g(x))'=f'(g(x))\cdot g'(x)=\frac{4}{2\sqrt{4g(x)+7}}\cdot e^{x+4}=\frac{2e^{x+4}}{\sqrt{4e^{x+4}+7}}$
