Question

Implicit differentiation.
I'm getting stuck on how to solve this problem

x^2y+y^2x=-2

Answer 1

Did you at least try differentiating it yet?

Answer 2

yeah, i used product rule but i couldn't factor out the dy/dx properly

Answer 3

If I differentiated it properly it's \((2xy+x^2y')+(2yy'x+y^2)=0\)
Whoops, kind of already did it for him >.<
But am I right?

Answer 4

Yeah that's how far I got

Answer 5

Move anything that doesn't have a y' to right

Answer 6

*to the right

Answer 7

So that would have the y^2 and 2xy on the right side of the equation and then when you factor out the y' on the left, divide?

Answer 8

Yup: \((2xy+x^2y')+(2yy'x+y^2)=0\)

\(x^2y'+2yy'x=-y^2-2xy\)

\(y'(x^2+2y)=-y^2-2xy\)
And just divide and you're done.

Answer 9

Should be 2yx not 2y, my mistake.

Answer 10

Thank you so much for that, I've been stuck on this for a while now. :)

Answer 11

You're welcome, and good luck :)