# How do you find the derivative of (1-y^2)^(1/2)?

Feb 23, 2017

$- \frac{y}{\sqrt{1 - {y}^{2}}}$

#### Explanation:

Use the power rule and chain rule: $\left({u}^{n}\right) ' = n {u}^{n - 1} u '$

$n = \frac{1}{2}$ so $n - 1 = - \frac{1}{2}$; $u = 1 - {y}^{2}$, so $u ' = - 2 y$

Using substitution, the derivative is:

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