Implicit differentiation?

Question

What is the derivative of x^2y^3-2xy^2+3x^2y=2xy

Answer 1

Best Answer - Chosen by Voters

x²y³ - 2xy² + 3x²y = 2xy

Use the product rule with terms containing x and y

2xy³ + 3x²y² dy/dx - (2y² + 4xy dy/dx) + 6xy + 3x² dy/dx = 0

2xy³ + 3x²y² dy/dx - 2y² - 4xy dy/dx + 6xy + 3x² dy/dx = 0

(3x²y² - 4xy + 3x²) dy/dx + (2xy³ - 2y² + 6xy) = 0

dy/dx = (2y² - 2xy³ - 6xy) / (3x²y² - 4xy + 3x²)