# What is the derivative of sqrt(x-3)?

Feb 7, 2016

$\frac{1}{2 \sqrt{x - 3}}$

#### Explanation:

The power rule states that $\frac{d}{\mathrm{dx}} {\left[u \left(x\right)\right]}^{n} = n {\left[u \left(x\right)\right]}^{n - 1} \cdot \frac{\mathrm{du}}{\mathrm{dx}}$.

Thus, application of this rule yields

$\frac{d}{\mathrm{dx}} \left[\sqrt{x - 3}\right] = \frac{d}{\mathrm{dx}} {\left(x - 3\right)}^{\frac{1}{2}}$

$= \frac{1}{2} {\left(x - 3\right)}^{- \frac{1}{2}} \cdot \left(1\right)$