# What is the derivative of (1 - x)^0.5?

Jul 23, 2018

$y = {\left(1 - x\right)}^{0.5} = {\left(1 - x\right)}^{\frac{1}{2}} = \sqrt{1 - x}$

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

#### Explanation:

Let ,

$y = {\left(1 - x\right)}^{0.5}$

$\therefore y = {\left(1 - x\right)}^{\frac{1}{2}}$

$\implies \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{2} {\left(1 - x\right)}^{\frac{1}{2} - 1} \frac{d}{\mathrm{dx}} \left(1 - x\right)$

$\implies \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{2} {\left(1 - x\right)}^{- \frac{1}{2}} \left(- 1\right)$

$\implies \frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{1}{2 {\left(1 - x\right)}^{\frac{1}{2}}} = - \frac{1}{2 \sqrt{1 - x}}$