# How do you find the derivative of sqrt(x - 2)?

Jun 28, 2016

Using the chain rule.

#### Explanation:

Write as a composition of two functions:

Let your function be $f \left(x\right)$, then $y = {u}^{\frac{1}{2}}$ and $u = x - 2$.

The chain rule states $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\mathrm{du}} \times \frac{\mathrm{du}}{\mathrm{dx}}$.

Differentiating y:

$y ' = \frac{1}{2} {u}^{\frac{1}{2} - 1}$

$y ' = \frac{1}{2} {u}^{- \frac{1}{2}}$

y' = 1/(2u^(1/2)

Differentiating u:

$u ' = 1 {x}^{1 - 1}$

$u ' = 1 {x}^{0}$

$u ' = 1$

Multiplying these two derivatives:

dy/dx = 1 xx 1/(2u^(1/2)

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{2 \sqrt{x - 2}}$

Hopefully this helps!