Use this equation to find dy/dx: 3y cos (x) = x2 + y2
Answer: The differential of the equation 3y cos (x) = x2 + y2, with respect to x is dy/dx = (3y sin x + 2x) / (3cos x - 2y).
Let's solve step by step to calculate dy/dx.
Given that 3y cos (x) = x2 + y2
Differentiating both sides with respect to x, we get
3 dy/dx cos x - 3y sin x = 2x + 2y dy/dx
⇒ 3 dy/dx cos x - 2y dy/dx = 2x + 3y sin x
By taking dy/dx common, we get
⇒ dy/dx (3 cos x - 2y) = 2x + 3y sin x
⇒ dy/dx = (2x + 3y sin x) / (3cos x - 2y)