A) \[x+y\]
B) \[x/y\]
C) \[y/x\]
D) \[x-y\]
Correct Answer: C
Solution :
\[{{x}^{m}}{{y}^{n}}=2{{(x+y)}^{m+n}}\Rightarrow m\log x+n\log y=\log 2+(m+n)\log (x+y)\] Differentiating both sides w.r.t. x, \[\frac{m}{x}+\frac{n}{y}\,\frac{dy}{dx}=\frac{m+n}{x+y}\left[ 1+\frac{dy}{dx} \right]\]Þ \[\frac{dy}{dx}=\frac{y}{x}\].
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