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Given that y2+xy=5,finddydx...

Given that y2+xy=5,finddydx

A.

y2y+x

B.

y2y+x

C.

y2yx

D.

y2y+x

Correct answer is B

y2+xy=5

By implicit differentiation

=2ydydx+y+xdydx=0

=2ydydx+xdydx=y

Factor out dydx

=dydx(2y+x)=y

∴\frac{dy}{dx}=\frac{-y}{2y + x}