Differentiation Problem

1. Dec 16, 2008

drandhawa

1. The problem statement, all variables and given/known data
If y^2 - 2xy=21, then dy/dx at the point (2,-3) is ?

2. Relevant equations
y^2 - 2xy=21

3. The attempt at a solution
I know that I have to differentiate the function. I just do not know how to do it: implicitly or explicitly.

2. Dec 16, 2008

HallsofIvy

Why not try both ways?

Actually, you should get the same (correct) answer doing either.)

3. Dec 16, 2008

drandhawa

i tried to diff it in terms of dy/dx but I don't think i got it right. i got dy/dx to equal 2y+2x

4. Dec 16, 2008

drandhawa

what I did was...
y^2= 2xy +21
2dy/dx=2(y+x(dy/dx))
2(dy/dx)= 2y+2x(dy/dx)
Divide by dy/dx on both sides
dy/dx=2y+2x

5. Dec 16, 2008

drandhawa

Never mind, I see what I did wrong. I should have put the two dy/dx's on the same side, take out dy/dx and then just divide to get dy/dx alone.

6. Dec 16, 2008

rl.bhat

y^2= 2xy +21
2dy/dx=2(y+x(dy/dx))

This step is wrong. It should be
2y*dy/dx = 2(y+x(dy/dx))