Question

If $xy=e^{x-y}$, find $\frac{dy}{dx}$

Answer 1

Consider the given equation.

$xy=e^{x-y}$ .....….. (1)

On differentiating both sides, we get

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

$y+x\frac{dy}{dx}=e^{x-y}-e^{x-y}\frac{dy}{dx}$

$(x+e^{x-y})\frac{dy}{dx}=e^{x-y}-y$

$\frac{dy}{dx}=\frac{e^{x-y}-y}{e^{x-y}+x}$

Hence, this is the answer.