Differentiate The Following Function With Respect To X. X^2e^xlog X .

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SolveGuidesJoin / LoginUse appLogin0You visited us 0 times! Enjoying our articles? Unlock Full Access!Standard XIApplied MathematicsRules of differentiationQuestionDifferentiate the following function with respect to x.$$x^2e^xlog x$$.A$$xe^x(1+x log x)$$.B$$xe^x(1+x log x+2 log x)$$.C$$xe^x(x log x+2 log x)$$.D$$xe^x(1+2 log x)$$.Open in AppSolutionVerified by Toppr

Correct option is D. $$xe^x(1+x log x+2 log x)$$.Given expression $$x^2e^x\log x$$differentiating w.r.t. $$x$$, we get$$\dfrac d{dx}(x^2e^x\log x)$$$$=x^2e^x\dfrac d{dx}\log x+x^2\log x\dfrac d{dx}e^x+e^x \log x\dfrac d{dx}(x^2) $$$$=x^2e^x\left(\dfrac 1x\right)+x^2e^x\log x+2xe^x\log x$$$$=xe^x(1+x\log x+2\log x)$$

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