I am having trouble differentiating x^2 + 2lny = y (solving for dy/dx). I know that I need to do implicit differentiation, but the answer I get is not correct. The answer I got was (2x-2xy)/2, but the answer is (2xy)/(y-2). How do I do this problem?

Answer 1

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

Answer 2

Thank you! Now I understand that I should've multiplied by y instead of moving the whole "2/y (dy/dx)" to the other side of the equation and then factor the dy/dx out. I can't believe how such a simple manuever can make the problem so much easier to solve. Thanks again!