Find dy/dx given that y^3+y^2-5y-x^2=-4

Answer 1

To find dy/dx, we will differentiate both sides of the given equation with respect to x.

Using the chain rule, we have d(y^3)/dx = 3y^2 * dy/dx and d(y^2)/dx = 2y * dy/dx. Additionally, the derivative of -5y with respect to x is -5(dy/dx), and the derivative of -x^2 is -2x.

So, differentiating both sides of the equation, we have:

3y^2 * dy/dx + 2y * dy/dx - 5(dy/dx) - 2x = 0

Simplifying this equation, we can combine like terms:

dy/dx(3y^2 + 2y - 5) - 2x = 0

Now, we solve for dy/dx:

dy/dx = 2x / (3y^2 + 2y - 5)