A) \[(log\text{ }2)\text{ }(log\text{ }3)\]
B) \[(log\text{ 18})\]
C) \[(log\text{ 1}{{\text{8}}^{2}}){{y}^{2}}\]
D) \[(log\text{ 18})y\]
E) \[{{(log\text{ 18})}^{2}}y\]
Correct Answer: D
Solution :
\[y={{2}^{x}}{{.3}^{2x-1}}\] On differentiating w.r.t.\[x,\]we get \[\frac{dy}{dx}={{2}^{x}}{{.3}^{2x-1}}2\log 3+{{3}^{2x-1}}{{.2}^{x}}\log 2\] \[={{2}^{x}}{{3}^{2x-1}}\log 18=y\log 18\]
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