If $y=x^{\log _{\mathrm{e}} x}$, then $\frac{d y}{d x}$ equals

$x^{\left(\log _{\mathrm{e}} x-1\right)} \cdot \log _e x$

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

y=x^{\log _{\mathrm{e}} x}

, then

\frac{d y}{d x}

equals

View answer and explanation

Correct option: A

2 x^{\left(\log _a x-1\right)} \cdot \log _e x

Option A (

2 x^{\left(\log _a x-1\right)} \cdot \log _e x

) is correct because by applying logarithmic differentiation, we can find the derivative of the given function.

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