# Use this equation to find dy/dx: 4y cos (x) = x^{2} + y^{2 }

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

## Answer: The differential of the equation 4y cos (x) = x^{2} + y^{2}, with respect to x is dy/ dx = (4y sin x + 2x) / (4cos x - 2y).

Let's solve step by step to find dy/dx.

**Explanation:**

Given that, 4y cos (x) = x^{2} + y^{2}

Differentiating both sides with respect to x, we get

4 dy/dx cos x - 4y sin x = 2x + 2y dy/dx

⇒ 4 dy/dx cos x - 2y dy/dx = 2x + 4y sin x

By taking dy/dx common, we get

⇒ dy/dx (4 cos x - 2y) = 2x + 4y sin x

⇒ dy/dx = (2x + 4y sin x) / (4cos x - 2y)