#### Answer

Please see explanation in "step-by-step"

#### Work Step by Step

Let $f(x)=x^{n}$.
Then,
$y=f[g(x)]=[g(x)]^{n}\quad $ is a composite function.
To find $\displaystyle \frac{dy}{dx}$, we use the chain rule,
$\displaystyle \frac{dy}{dx}=f^{\prime}[g(x)]\cdot g^{\prime}(x)$.
By the power rule$, f^{\prime}(x)=nx^{n-1}$, so
$\displaystyle \frac{dy}{dx}=n[g(x)]^{n-1}\cdot g^{\prime}(x)$.