A) \[\frac{dy}{dx}=\left( \frac{y}{x} \right)\log x\]
B) \[\frac{dy}{dx}=\left( \frac{x}{y} \right)\log y\]
C) \[\frac{dy}{dx}=\left( \frac{y}{x} \right)\log y\]
D) \[\frac{dy}{dx}=\left( \frac{x}{y} \right)\log x\]
Correct Answer: C
Solution :
\[y={{e}^{mx}}\] Þ \[\log y=mx\Rightarrow m=\frac{\log y}{x}\] Now \[y={{e}^{mx}}\] Þ \[\frac{dy}{dx}=m{{e}^{mx}}=\frac{\log y}{x}.y=\left( \frac{y}{x} \right)\log y\].
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