How do i do this question? I get the reverse

[link2110]

Homework Statement

find dy/dx
yx²+ xy²=7

Homework Equations

The Attempt at a Solution

xy(x+y)=7
2xy=(x+y) (x+y) = 7
2xy + x²+2xy +y²=0
2xy + dx/dy(x²+2xy+y²)=0
2xy +x²+dy/dx 2xy + dy/dx y²
dy/dx = (-2xy-x²)/(2xy + y²)

The answer is actually (-y²+2xy)/(x²+2xy)

Can anybody tell me what I'm doing wrong/how to swap the answer?

 

[FanofAFan]

don't factor out xy, and just use product rule, and then 7 is just zero and go from there... i seriously think you are making it harder than it should be.

 

[link2110]

x²y + xy²=7
[x² + 2xy] + [2yx + y²] = 0

So that's what i get to, but where do i distribute d/dx into?

 

[FanofAFan]

Naw dude... its [x²dy/dx + 2xy] + [2y(dy/dx)x + y²] = 0

then subtract the non dy/dx values and then factor out dy/dx and you are done!

 

[link2110]

so for [x²dy/dx + 2xy]
why is the dy/dx on the first term?

 

[FanofAFan]

because it is the d/dx for y is just dy/dx... which is just the derivative for y in terms of x... its an implicit derivative (ie not expressed directly in terms of the independent variable)

so y³ = 3y²(dy/dx)

 

[link2110]

oh i get it now, thanks!