If $e^{x^2y} = C$, then $\frac{dy}{dx}$ is:

$\frac{-2y}{x}$

The correct answer is Option (2) → $\frac{-2y}{x}$ ##

Given, $e^{x^2y} = C$.

Differentiating w.r.t. $x$:

$\frac{d}{dx}(e^{x^2y}) = \frac{d}{dx}(C)$

$e^{x^2y} \left[ x^2 \frac{dy}{dx} + y(2x) \right] = 0$

$x^2 e^{x^2y} \frac{dy}{dx} + 2xy e^{x^2y} = 0$

$x^2 e^{x^2y} \frac{dy}{dx} = -2xy e^{x^2y}$

$\frac{dy}{dx} = \frac{-2xy e^{x^2y}}{x^2 e^{x^2y}} = \frac{-2y}{x}$