Use this equation to find dy/dx: 9y cos (x) = x² + y² 

We can make use of uv (product rule) method of differentiation to solve the given question.

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.

Explanation:

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)

Thus, the differential of the equation  9y cos(x) = x² + y², with respect to x is dy/dx = (2x + 9y sin x) / (9cos x - 2y).