Implicit Differentiation problem

Question

Consider the following.

xy + 2x + 2x² = 2

(a) Find y' by implicit differentiation.

(b) Solve the equation explicitly for y and differentiate to get y' in terms of x.

(c) Check that your solutions to part (a) and (b) are consistent by substituting the expression for y into your solution for part (a).

Answer 1

xy' + y + 2 + 4x = 0

xy' = -y - 2 - 4x

y' = -y/x - 2/x - 4