What is the derivative of

Question

xy^2 +y^3= x^2?

Answer 1

The equation is xy² + y³ = x².

Differentiate the above equation with respect to x.

(xy²)' + (y³)' = (x²)'

Apply product rule of derivative : (uv)' = uv' + vu'.

x(y²)' + (y²)(x)'+ (y³)' = (x²)'

Apply power rule of derivative : (xⁿ)' = nx^{n - 1}.

x(2y)y' + (y²)(1)+ 3y²y' = 2x

2xyy' + y²+ 3y²y' = 2x

y'(2xy + 3y²) = (2x - y²)

y' = (2x - y²) / (2xy + 3y²).