Derivative of x raised to the power x

Question

For $x>0$ , find $\dfrac{d}{dx}\,x^x$ .

$x^x(1+\ln x)$ . Write $x^x=e^{x\ln x}$ and use the chain rule: the derivative of the exponent $x\ln x$ is $\ln x+1$ .

Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q6.18, p.191; question and answer rewritten by SelfMadeQuant.com.

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