Question

Find the derivative of $\sqrt{x}+\sqrt{y}=9$ at $(4,9)$

Answer 1

We have,

$\begin{array}{c}\sqrt{x}+\sqrt{y}=9\\ \frac{1}{2\sqrt{x}}+\frac{1}{2\sqrt{y}}\frac{dy}{dx}=0\\ \frac{1}{\sqrt{y}}\frac{dy}{dx}=\frac{-1}{\sqrt{x}}\\ \frac{dy}{dx}=\frac{-\sqrt{y}}{\sqrt{x}}\\ =\frac{-\sqrt{9}}{\sqrt{4}}\\ =\frac{-3}{2}\end{array}$