If $y=(\log x)^x+x^{\log x}$, then $\frac{d y}{d x}=$

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

y=(\log x)^x+x^{\log x}

, then

\frac{d y}{d x}=

View answer and explanation

Correct option: A

(\log x)^x\left[\log (\log x)+\frac{1}{\log x}\right]+x^{\log x} \cdot\left(\frac{2 \log x}{x}\right)

Option A is correct because it accurately applies the chain rule and logarithmic differentiation to find the derivative of the given function.

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