Question

Use implicit differentiation to find dy/dx.

2xy-y^2=1

Answer 1

\[(product. rule)-(na^{n-1})=0\]

Answer 2

\[2(xy'+y)-2yy'=0\] solve for \(y'\)

Answer 3

you can think of it as having
\[2xf(x)-f^2(x)=0\] and being asked to solve for \(f'(x)\)

Answer 4

product and chain rule gives the result

Answer 5

so is the derivative just
2xy-2y?

Answer 6

this answer choices are
\[A. \frac{ y }{ y-x }\]
\[B. \frac{ x }{ x-y }\]
\[C. \frac{ x }{ y-x }\]
\[D. \frac{ y }{ x-y }\]

Answer 7

but how do they get one of the four choices