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.

A bit of  trickery :
$y:= (4e^{x+4}+7)^{1/2};$
$y^2= 4e^{x+4} +7.$
Differentiating both sides with resp. to x:
$2y\dfrac{dy}{dx} = 4e^{x+4};$
$\dfrac {dy}{dx}= \dfrac {4e^{x+4}}{2y};$
$\dfrac {dy}{dx} = \dfrac {2e^{x+4}}{(4e^{x+4}+7)^{1/2}}.$
