question_answer

lf \[y={{x}^{n}}\,\,\log x+x\,\,{{(\log \,\,x)}^{n}},\] then\[\frac{dy}{dx}=\]

A)  \[{{x}^{n-1}}\,\,(1+n\,\,\log \,\,x)+{{(\log \,\,x)}^{n-1}}[n+\log \,\,x]\]

B)  \[{{x}^{n-2}}\,\,(1+n\,\,\log \,\,x)+{{(\log \,\,x)}^{n-1}}[n+\log \,\,x]\]

C)  \[{{x}^{n-1}}\,\,(1+n\,\,\log \,\,x)+{{(\log \,\,x)}^{n-1}}[n-\log \,\,x]\]

D)  \[{{x}^{n-2}}(1-n\,\,\log \,\,x)+{{(\log \,\,x)}^{n-1}}[n-\log \,\,x]\]

E)  None of these