Posted by **W** on Wednesday, November 30, 2011 at 10:28pm.

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?

- Calculus -
**Reiny**, Wednesday, November 30, 2011 at 10:35pm
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)

- Calculus -
**W**, Wednesday, November 30, 2011 at 10:51pm
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!

## Answer This Question

## Related Questions

- calculus; implicit differentiation - Use implicit differentiation to find the ...
- Calculus 1 - implicit differentiation - I do not understand implicit ...
- Calculus 1 - implicit differentiation - I do not understand implicit ...
- calculus - Alright so implicit differentiation is just not working out for me. ...
- Calculus: implicit differentiation - Find dy/dx by implicit differentiation 1. x...
- calculus - Given y^4 -x^4=16 find and simplify d2y/dx2 using implicit ...
- Calculus Help and Check - Find dy/dx by implicit differentiation. x^5(x + y) = ...
- Calculus 1 Implicit differentiation - Help please help me understand what i am ...
- Calculus - Hi, I'm having trouble using implicit differentiation to determine dy...
- Calculus Help STEVE - find y'' by implicit differentiation. 2x^3 + 3y^3 = 8 I ...

More Related Questions