Calculus and Its Applications, Chapter 1, 1.5, Section 1.5, Problem 16

If $y = 4 \sqrt{x}$, determine $\displaystyle \frac{dy}{dx}$

$
\begin{equation}
\begin{aligned}
\frac{d}{dx}(4 \sqrt{x}) &= 4 \cdot \frac{d}{dx} \left( x^{\frac{1}{2}} \right) \\
\\
&= 4 \cdot \frac{1}{2}x^{\frac{1}{2}-1}\\
\\
&= 2x^{-\frac{1}{2}}\\
\\
&= \frac{2}{\sqrt{x}}
\end{aligned}
\end{equation}
$