If ${\mathrm{xe}}^{\mathrm{y}}=1$, then the value of $\frac{\mathrm{dy}}{\mathrm{d}x}$ at $\mathrm{x}=1$ is :

Question

YESPYQ · Accepted Answer

Correct answer: a) -1. $\frac{d}{dx}\left(x{e}^{y}\right)=\frac{d}{dx}(1)$ ${e}^{y}+x{e}^{y}\frac{dy}{dx}=0$ $\frac{dy}{dx}=\frac{-{e}^{y}}{x{e}^{y}}$ $\frac{dy}{dx}=-\frac{1}{x}$ ${\left.\frac{dy}{dx}\right|}_{x=1}=-\frac{1}{1}=-1$

If \({\mathrm{xe}}^{\mathrm{y}}=1\), then the value of \(\frac{\mathrm{dy}}{\mathrm{d}x}\) at \(\mathrm{x}=1\) is :

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