Question

If $\sqrt{x}+\sqrt{y}=5$ then $\frac{dy}{dx}at(4,9)=?$

Answer 1

$\sqrt{x}+\sqrt{y}=5$

$\Rightarrow \frac{1}{2}+\frac{1}{2\sqrt{y}}\frac{dy}{dx}=0\Rightarrow \frac{dy}{dx}=\frac{-\sqrt{y}}{\sqrt{x}}$

${\frac{dy}{dx}}_{x=4,y=9}=\frac{-\sqrt{9}}{\sqrt{4}}=\frac{-3}{2}$