A) \[\frac{{{e}^{x}}}{x}\]
B) \[{{e}^{x}}\left( \frac{1}{x}+x\log x \right)\]
C) \[{{e}^{x}}\left( \frac{1}{x}+\log x \right)\]
D) \[\frac{{{e}^{x}}}{\log x}\]
Correct Answer: C
Solution :
Differentiating \[y={{e}^{x}}\log x,\] w.r.t. x ,we get \[\frac{dy}{dx}={{e}^{x}}\times \frac{1}{x}+\log x\times {{e}^{x}}={{e}^{x}}\left( \frac{1}{x}+\log x \right)\].
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