Question

Find $\frac{dy}{dx}$ if $xy=e^{x-y}$

Answer 1

$xy=e^{x-y}$ (Differentiating both sides)

$y+xy{y}^{‵}=e^{x-y}(1-y^{‵})y+xy{y}^{‵}=e^{x-y}-e^{x-y}\times y^{‵}{y}^{‵}(xy+e^{x-y})=e^{x-y}-y{y}^{‵}=\frac{e^{x-y}-y}{xy+e^{x-y}}$