# How do you find the derivative for 1/sqrt(1-x^2)?

Mar 30, 2015

The answer is: $\frac{x}{\sqrt{{\left(1 - {x}^{2}\right)}^{3}}}$.

This is because the function can be written:

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

So:

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

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