Question

Use this equation to find dy/dx. 3y cos x = x2 + y2

Answer 1

Given: 3y cos x = x² + y²

Define $y' = \frac{dy}{dx}$

Then by implicit differentiation, obtain
3y' cos(x) - 3y sin(x) = 2x + 2y y'
y' [3 cos(x) - 2y] = 2x + 3y sinx)

Answer:
$\frac{dy}{dx} = \frac{2x+3y \, sin(x)}{3cos(x)-2y}$