What is the derivative of y with respect to x at the point (2,-3)?

[drandhawa]

Homework Statement

If y^2 - 2xy=21, then dy/dx at the point (2,-3) is ?

Homework Equations

y^2 - 2xy=21

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.

 

[HallsofIvy]

Why not try both ways?

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

 

[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

 

[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

 

[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.

 

[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))