If $x^{\frac{3}{4}}+y^{\frac{3}{4}}=\pi$, then the value of $\frac{d y}{d x}$ is:

$\sqrt[-4]{\frac{y}{x}}$

The correct answer is Option (4) → $\sqrt[-4]{\frac{y}{x}}$

$x^{3/4} + y^{3/4} = \pi$

$\frac{3}{4}x^{-1/4} + \frac{3}{4}y^{-1/4}\frac{dy}{dx} = 0$

$x^{-1/4} + y^{-1/4}\frac{dy}{dx} = 0$

$\frac{dy}{dx} = -\frac{x^{-1/4}}{y^{-1/4}}$

$= -\frac{y^{1/4}}{x^{1/4}}$

$\frac{dy}{dx} = -\frac{y^{1/4}}{x^{1/4}}$