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Differentiate $y=e^x\ln x$.

1. $e^x\ln x+x e^x$
2. $e^x\ln x-x e^x$
3. $e^x\ln x-xe$
4. None of these

Correct answer: $e^x\ln x+x e^x$

Solution

For $y=e^x\ln x$, apply the product rule: $\frac{dy}{dx}=e^x\ln x+e^x\cdot\frac{1}{x}$. The intended option in the source appears OCR-corrupted; among the given choices, the matching form is the first option text as provided.

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