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If y2+xyx=0, find \(\frac{\mathrm d y}{\mathrm...

If y2+xyx=0, find dydx.

A.

1y2y

B.

12yx

C.

1yx+2y

D.

1x+2y

Correct answer is C

Given y2+xyx=0

Using the method of implicit differentiation, we have

2ydydx+xdydx+y1=0

dydx(2y+x)=1y

dydx=1yx+2y