Question

If $\sqrt{x}+\sqrt{y}=10$, find $\frac{dy}{dx}$ at $y=4$.

• A. $4$
• B. $-3$
• C. $-4$
• D. $3$

Answer 1

The correct option is C $-4$

Given equation is $\sqrt{x}+\sqrt{y}=10$
$\frac{1}{2\sqrt{x}}\frac{dx}{dy}+\frac{1}{2\sqrt{y}}=0$
$\Rightarrow \frac{dx}{dy}=-\frac{\sqrt{x}}{\sqrt{y}}=-\frac{10-\sqrt{y}}{\sqrt{y}}$
$\Rightarrow \frac{dx}{dy}=\frac{\sqrt{y}-10}{\sqrt{y}}$
$\Rightarrow {\left(\frac{dx}{dy}\right)}_{y=4}=\frac{2-10}{2}=\frac{-8}{2}=-4$