If $x^{\frac{3}{4}}+y^{\frac{3}{4}}=a^{\frac{3}{4}}$ (a is a constant) then $\frac{dy}{dx}$ is equal to :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $-\left(\frac{y}{x}\right)^{\frac{1}{4}}$
$x^{\frac{3}{4}}+y^{\frac{3}{4}}=a^{\frac{3}{4}}$
Taking differentiation both sides,
$\frac{3}{4}x^{-\frac{1}{4}}+\frac{3}{4}y^{-\frac{1}{4}}\left(\frac{dy}{dx}\right)=0$
$\frac{dy}{dx}=-\left(\frac{y}{x}\right)^{\frac{1}{4}}$