Find the derivative of the function f:(0,oo)->R, f(x)=x^x.
The domain of the function allows us to write f(x)=xx as f(x)=eln(x^x)=ex ln(x) (since ln(x) is defined on (0,oo) only). Using the standard derivative rules we get f'(x)=ex ln(x) (x ln(x))'=ex ln(x)(1+ln(x))=xx (1+ln(x)).
AR
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