If $e^{x^2y} = C$, then $\frac{dy}{dx}$ is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{-2y}{x}$ ##
Given, $e^{x^2y} = C$.
Differentiating w.r.t. $x$:
$\frac{d}{dx}(e^{x^2y}) = \frac{d}{dx}(C)$
$e^{x^2y} \left[ x^2 \frac{dy}{dx} + y(2x) \right] = 0$
$x^2 e^{x^2y} \frac{dy}{dx} + 2xy e^{x^2y} = 0$
$x^2 e^{x^2y} \frac{dy}{dx} = -2xy e^{x^2y}$
$\frac{dy}{dx} = \frac{-2xy e^{x^2y}}{x^2 e^{x^2y}} = \frac{-2y}{x}$