A) \[\frac{2xy}{2y-{{x}^{2}}}\]
B) \[\frac{xy}{y+{{x}^{2}}}\]
C) \[\frac{xy}{y-{{x}^{2}}}\]
D) \[\frac{2xy}{2+\frac{{{x}^{2}}}{y}}\]
Correct Answer: A
Solution :
\[y={{x}^{2}}+\frac{1}{y}\Rightarrow {{y}^{2}}={{x}^{2}}y+1\] \[\Rightarrow 2y\frac{dy}{dx}=y.2x+{{x}^{2}}\frac{dy}{dx}\]Þ \[\frac{dy}{dx}=\frac{2xy}{2y-{{x}^{2}}}\].
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