Question

finde the derivative of x^2*(x-y)^2=X^2- Y^2

Answer 1

wrt \(x\)?

Answer 2

the right hand side is easiest, you get \(2x-2yy'\)

Answer 3

the left hand side requires the product rule

Answer 4

\[2x(x-y)^2+x^2\left(2(x-y)(1-y')\right)\]

Answer 5

set
\[2x(x-y)^2+x^2\left(2(x-y)(1-y')\right)=2x-2yy'\] and to a raft of algebra to solve for \(y'\)

Answer 6

\[\frac{ -2x^3+3x^2y-xy^2+x }{ x^2y-x^3+y }\]

Answer 7

like that?

Answer 8

lol i have no idea

Answer 9

i can't do all that algebra without making a mistake
you can check your answer here
http://www.wolframalpha.com/input/?i=x^2*%28x-y%29^2%3Dx^2-+y^2+
look at the very bottom for \(\frac{\delta y(x)}{\delta(x)}\)