Question

Find dy/dx by implicit differentiation.
x^3 - 3x^2y + 2xy^2 =12

Please show me the work/steps on how to do it.

Answer 1

x^3 - (3x^2)(y) + (2x)(y^2) =12

use the product rule on the 2nd and 3rd term

3x^2 - 3x^2 dy/dx - 6xy + 2x (2y)dy/dx + 2y^2 = 0
dy/dx(4xy - 3x^2) = 6xy - 3x^2 - 2y^2

dy/dx = (6xy - 3x^2 - 2y^2))/(4xy - 3x^2)