Question

If $\sqrt{xy}=e^{(x-y)}$.Find $\frac{dy}{dx}$

Answer 1

Given $\sqrt{xy}=e^{x-y}⟹\frac{1}{2}(\log x+\log y)=x-y$

Differentiating on both sides

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

$(\frac{1}{y}+2)\frac{dy}{dx}=2-\frac{1}{x}$

$\frac{dy}{dx}=\frac{y(2x-1)}{x(2y+1)}$