Use this equation to find dy/dx: 9y cos (x) = x2 + y2
Answer: The differential of the equation 9y cos (x) = x2 + y2, with respect to x is dy/dx = (9ysin x + 2x) / (9cos x - 2y).
Let's solve step by step to find dy/dx.
Given that 9y cos (x) = x2 + y2
Differentiating both sides with respect to x, we get
9 dy/dx cos x - 9y sin x = 2x + 2y dy/dx
⇒ 9 dy/dx cos x - 2y dy/dx = 2x + 9y sin x
By taking dy/dx common, we get
⇒ dy/dx (9 cos x - 2y) = 2x + 9y sin x
⇒ dy/dx = (2x + 9y sin x) / (9cos x - 2y)