# Homework Help: Implicit Differentation

1. Feb 14, 2009

### Jim4592

1. The problem statement, all variables and given/known data
find dy/dx for x2y+xy2=6

2. Relevant equations

3. The attempt at a solution
d/dx (x2y+xy2) = d/dx (6)
x2*(dy/dx)+y*2x+x*2y(dy/dx)+2y=0
x2*(dy/dx)+y*2x+x*2y(dy/dx)=-2y
(dy/dx)+y*2x+x*2y(dy/dx)=(-2y/x2)
(dy/dx)+y*2x+(dy/dx)=(-2y/x2+2xy)

I'm not sure what to do now, i know that the answer is (2xy-y2/x2+2xy)

I got the denominator correct in my answer but i'm not sure how to get the numerator correctly. Did I go wrong somewhere during the process?

2. Feb 14, 2009

### Tom Mattson

Staff Emeritus
Now you algebraically solve for dy/dx.

3. Feb 14, 2009

### Unco

Try that again. Piece by piece:
$$x^2y$$ differentiates to $$2xy + x^2y'$$
$$xy^2$$ differentiates to $$y^2 + 2xyy'$$

4. Feb 14, 2009

### tiny-tim

Hi Jim4592!

Isn't it (2xy + y2/x2+2xy)?

5. Feb 14, 2009

### Unco

Rather,

-(2xy + y2)/(x2 + 2xy)

6. Feb 14, 2009

### tiny-tim

oops!

thanks, Unco!