A) \[\frac{2xy}{2y-{{x}^{2}}}\]
B) \[\frac{xy}{y+{{x}^{2}}}\]
C) \[\frac{xy}{y-{{x}^{2}}}\]
D) \[\frac{2x}{2+\frac{{{x}^{2}}}{y}}\]
Correct Answer: A
Solution :
Given equation can be written as \[y={{x}^{2}}+\frac{1}{y}\Rightarrow {{y}^{2}}={{x}^{2}}y+1\] On differentiating w. r. t x, we get \[2y\frac{dy}{dx}={{x}^{2}}\frac{dy}{dx}+2xy+0\] \[\Rightarrow \frac{dy}{dx}(2y-{{x}^{2}})=2xy\] \[\Rightarrow \] \[\frac{dy}{dx}=\frac{2xy}{2y-{{x}^{2}}}\]
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