## Calculus with Applications (10th Edition)

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 $\displaystyle \frac{dy}{dx}=n[g(x)]^{n-1}\cdot g^{\prime}(x)$.