What is the implicit derivative of 1=xy^2-y^2+x^2 ?

1 Answer
Feb 1, 2017

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

Explanation:

Assuming y is a function of x and not the opposite:

Differentiate both sides with respect to x.

(x^2 - y^2 + xy^2)' = (1)'

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

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

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

(If f is a function of y, then (df)/(dx) = (df)/(dy) (dy)/(dx))