A) \[{{x}^{2}}/{{y}^{2}}\]
B) \[-{{x}^{2}}/{{y}^{2}}\]
C) \[{{y}^{2}}/{{x}^{2}}\]
D) \[-{{y}^{2}}/{{x}^{2}}\]
Correct Answer: D
Solution :
[d] \[\log c+\log \left| x \right|=\frac{x}{y}\] Differentiating w.r.t. x, \[\frac{1}{x}=\frac{y-x\frac{dy}{dx}}{{{y}^{2}}}\] Or \[\frac{{{y}^{2}}}{x}=y-x\frac{dy}{dx}\] Or \[\frac{dy}{dx}=\frac{y}{x}-\frac{{{y}^{2}}}{{{x}^{2}}}\] Or \[\phi \left( \frac{x}{y} \right)=-\frac{{{y}^{2}}}{{{x}^{2}}}\]
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