To find the answer, we use the Chain Rule. This states that if
$\displaystyle h(x)=g(f(x)),$
then
$\displaystyle h'(x)=g'(f(x))f'(x).$
A way of looking at this rule is to note that $\displaystyle f$ influences how fast $\displaystyle f(x)$ changes with $\displaystyle x$, which in turn affects the rate of change of $\displaystyle g(f(x))$ by a factor of $\displaystyle f'(x)$.
If $\displaystyle f(x)=2x$, for example, then $\displaystyle f(x)$ will change twice as fast as $\displaystyle x$, and the rate of change of $\displaystyle g(f(x))$ will be multiplied by a factor of $\displaystyle 2$.
Hope this helps!