# How do you find the derivative of sqrt(5x)?

If $u$ is a function, then the derivative of ${u}^{n}$ is $n \cdot u ' \cdot {u}^{n - 1}$. We apply this here.
$f \left(x\right) = \sqrt{5 x} = {\left(5 x\right)}^{\frac{1}{2}}$ so $f ' \left(x\right) = \frac{1}{2} \cdot 5 \cdot {\left(5 x\right)}^{\frac{1}{2} - 1} = \frac{5}{2 \sqrt{5 x}}$.