Question

find dy by dx of the following implicit function ycube minus 3y square xequal toxcube​

Answer 1

Step-by-step explanation:

Given implicit function is

$y^{3} - 3 {y}^{2}x = {x}^{3}$

Differentiating both side we get,

$3 {y}^{2} \frac{dy}{dx} - 3 {y}^{2} - 6xy \frac{dy}{dx} = 3 {x}^{2}$

Taking dy/dx common we get,

$(3 {y}^{2} - 6xy) \frac{dy}{dx} = 3 {x}^{2} + 3 {y}^{2}$

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

hope it helps you