How do you find the derivative of sqrt(1-x^2)?

Jul 20, 2016

$\frac{d y}{d x} = - \frac{x}{\sqrt{1 - {x}^{2}}}$

Explanation:

$y = \sqrt{1 - {x}^{2}}$

$\text{let us remember that : "y=sqrt u" ; } {y}^{'} = {u}^{'} / \left(2 \sqrt{u}\right)$

$\frac{d y}{d x} = - \frac{\cancel{2} x}{\cancel{2} \sqrt{1 - {x}^{2}}}$

$\frac{d y}{d x} = - \frac{x}{\sqrt{1 - {x}^{2}}}$