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