Answer
$\frac{dy}{dx}=\frac{-4}{12x^{1/5}y^{1/5}}$
Work Step by Step
Take the derivative of the equation on each side separately. Apply chain rule when differentiating the "y" variables since we are differentiating with respect to x:
$\frac{4}{5}\times5x^{-1/5}+\frac{6}{5}\times10y^{1/5}\frac{dy}{dx}=0$
Move all terms with dy/dx to one side of the equation, and isolate dy/dx:
$12y^{1/5}\frac{dy}{dx}=-4x^{-1/5}$
$\frac{dy}{dx}=\frac{-4x^{-1/5}}{12y^{1/5}}$
$\frac{dy}{dx}=\frac{-4}{12x^{1/5}y^{1/5}}$
