Use this equation to find dy/dx. 6y cos (x) = x² + y² 

We can make use of uv method of differentiation to solve the given question.

Answer: The differential of the equation  6y cos (x) = x² + y², with respect to x is dy/dx = (6ysin x + 2x) / (6cos x - 2y).

Let's look into the solution

Explanation:

Given: 6y cos (x) = x² + y²

Differentiating on both sides with respect to x, we get

6 dy/dx cos x - 6y sin x = 2x + 2y dy/dx

⇒ 6 dy/dx cos x - 2y dy/dx = 6y sin x +  2x

⇒ dy/dx (6 cos x - 2y) = 6y sin x + 2x

⇒ dy/dx = (6ysin x + 2x) / (6cos x - 2y)

Thus, the differential of the equation  6y cos(x) = x² + y², with respect to x is dy/dx = (6ysin x + 2x) / (6cos x - 2y).