This question is from a UNIVERSITY PAPER (just incase some of you ppl will ask why would you want to differentiate that) ....
how would i go on about this... the answer is x^x(1+ln(x)) ???????
Thank you....
Hi!
Write $\displaystyle x^{x} $ as $\displaystyle e^{x\cdot \ln(x)} $.
Now differentiate using normal rules, with $\displaystyle u(x)=x\cdot \ln(x) $ .
$\displaystyle \frac{d}{dx}(e^{u(x)})=e^{u}\cdot u'(x) = e^{x\cdot \ln(x)}\cdot(1+\ln(x) =x^{x}\cdot(1+\ln(x))$
Note that I used the product rule on $\displaystyle x\cdot \ln(x) $