# implicit differentiation

• May 1st 2011, 11:35 PM
mjfuentes85
implicit differentiation
so I have x*y^2 + x*y = sin y and i try to solve for y'.
So far I have x2yy' + y^2 + xy' + y = cosyy'.
It looks as though as I am going to factor out the y' on the left side of the equation and then divide both side by y' but I am going to lose my y'??? I am a little stuck. any help or steps so a solution would be appreciated.
-Marcus
• May 1st 2011, 11:46 PM
Prove It
Move everything that has a y' term to one side, then factorise and divide by the other factor.
• May 1st 2011, 11:48 PM
FernandoRevilla
Quote:

Originally Posted by mjfuentes85
So far I have x2yy' + y^2 + xy' + y = cosyy'.

Right, now

$\displaystyle y'=\dfrac{y^2+y}{\cos y-2xy-x}$

Edited: Sorry, I didn't see Prove It's post.
• May 1st 2011, 11:52 PM
mjfuentes85
can you show me the steps in between ?? I am missing the connection.

Never mind I was completely missing that you I should subtract both sides by cosyy' then factor out the y'. Thnx guys for your help
-Marcus