Question

Use this equation to find dy/dx. 8y cos(x) = x² + y² dy/dx=___

Answer 1

To find dy/dx, we differentiate both sides of the given equation and apply the product rule. Simplifying the equation, we can solve for dy/dx.

Step-by-step explanation:

The given equation is 8y cos(x) = x² + y². To find dy/dx, we need to differentiate both sides of the equation with respect to x. Applying the product rule on the left side gives us:

8(cos(x) * dy/dx * y) - 8y * sin(x) = 2x + 2y * dy/dx

Simplifying the equation, we get:

(8y * cos(x) - 2y) * dy/dx = 2x - 8y * sin(x)

Dividing both sides by (8y * cos(x) - 2y), we can find dy/dx:

dy/dx = (2x - 8y * sin(x)) / (8y * cos(x) - 2y)