Question

Regard y as the independent variable and x as the dependent variable and use implicit differentiation to find dx/dy. x3y2 − x4y + 2xy3 = 0

Answer 1

Hello, I was recently done with this chapter in my AP Calculus class and would love to help you. I am inferring some of the values since they are not clearly stated.
x^3 * y^2 - x^4*y + 2x *y^3 = 0
use the product rule
(3x^2 (dx/dy)* y^2) + (x^3 *2y) - (4x^3(dx/dy) * y) + (x^4 * 1) + 2((dx/dy) * y^3) + (x * 3y^2)) =0
group the commons with non commons
dx/dy(3x^2y^2 -4x^3y + 2y^3) = -2x^3y - 24xy^2 - x^4
dx/dy = (-2x^3y - 24xy^2 - x^4) / (3x^2y^2 -4x^3y + 2y^3).