A) \[\frac{y}{x}\]
B) \[-\frac{y}{x}\]
C) \[\frac{x}{y}\]
D) \[-\frac{x}{y}\]
Correct Answer: A
Solution :
Taking \[\log \]both sides, \[p\log x+q\log y=(p+q)\log (x+y)\] Þ \[\frac{p}{x}+\frac{q}{y}\frac{dy}{dx}=\frac{p+q}{x+y}\left( 1+\frac{dy}{dx} \right)\Rightarrow \frac{dy}{dx}=\frac{y}{x}\].
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