How do you use implicit differentiation to find (dy)/(dx) given sqrtx+sqrty=1?

Jul 24, 2016

$y ' = - \frac{\sqrt{y}}{\sqrt{x}} = 1 - \frac{1}{\sqrt{x}}$

Explanation:

$\frac{d}{\mathrm{dx}} \left(\sqrt{x} + \sqrt{y} = 1\right)$

$\implies \frac{1}{2 \sqrt{x}} + \frac{1}{2 \sqrt{y}} y ' = 0$

$y ' = - \frac{\sqrt{y}}{\sqrt{x}}$

$y ' = - \frac{1 - \sqrt{x}}{\sqrt{x}}$

$y ' = 1 - \frac{1}{\sqrt{x}}$