A) \[\left( 1+\log \,x \right)+\left( {{a}^{x}}\,\log \,a+a{{x}^{a-1}} \right)\]
B) \[{{x}^{x}}\left( 1+\log \,x \right)+\log \,a+a{{x}^{a-1}}\]
C) \[{{x}^{x}}\left( 1+\log \,x \right)+{{x}^{a}}\,\operatorname{logx}+a{{x}^{a-1}}\]
D) \[{{x}^{x}}\left( 1+\log \,x \right)+{{a}^{x}}\,\log \,a\,+\,a{{x}^{a-1}}\]
Correct Answer: D
Solution :
\[{{x}^{x}}\left( 1+\log \,x \right)+{{a}^{x}}\,\log \,a\,+\,a{{x}^{a-1}}\]
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