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If $xe^y = 1$, then the value of $\frac{dy}{dx}$ at $x = 1$ is: |
$-1$ $1$ $-e$ $-\frac{1}{e}$ |
$-1$ |
The correct answer is Option (1) → $-1$ ## We have $xe^y = 1$. Differentiating w.r.t. '$x$' both sides: $1 \cdot e^y + xe^y \frac{dy}{dx} = 0$ $xe^y \frac{dy}{dx} = -e^y$ $\frac{dy}{dx} = -\frac{1}{x}$ $∴\left. \frac{dy}{dx} \right|_{x=1} = -1$ |
