# How do you differentiate f(x)=1/sqrt(1-x) using the chain rule?

Apr 11, 2018

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

#### Explanation:

Rewrite using negative exponents:

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

Then, applying the Power Rule in conjunction with the Chain Rule,

$f ' \left(x\right) = - \frac{1}{2} {\left(1 - x\right)}^{- \frac{3}{2}} \cdot \frac{d}{\mathrm{dx}} \left(1 - x\right)$

$\frac{d}{\mathrm{dx}} \left(1 - x\right) = - 1 ,$ so we have

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

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