Derivative of x times the natural log of x

Question

Compute $\dfrac{d}{dx}\left(x\log x\right)$ for $x>0$ , where $\log$ is the natural logarithm.

$\log x+1$ . The product rule gives $1\cdot\log x+x\cdot\tfrac1x$ .

Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q6.21, p.191; question and answer rewritten by SelfMadeQuant.com.

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