Find dy/dx if y^2-3xy+x^2=7

Question

anonymous · Answer

y^2 - 3xy + x^2 = 7 // start
2y(dy/dx) - (3y + 3x(dy/dx)) + 2x = 0 //derive
2y(dy/dx) - 3y - 3x(dy/dx) + 2x = 0 //simplify product rule
2y(dy/dx) - 3x(dy/dx) = 3y - 2x // move -3y and 2x over
(dy/dx)(2y - 3x) = 3y - 2x // factor out dy/dx
dy/dx = (3y - 2x)/(2y - 3x) //divide, and you have your answer

anonymous · Answer

Thank you! Just wondering, but what happened to the "x" in the derive part? Shouldn't it be 2yy' -3xy'+3yx'+2x=0?

anonymous · Answer

Well, since it asks you to derive with respect to dy/dx or y', and NOT dx/dy or x', you can ignore it anytime you derive x.

anonymous · Answer

Oooh, okay! Thanks again, I really appreciate it. :)

anonymous · Answer

no problem :)