[tex]\displaystyle\bf\\
f(x)=x^x,~~~x\ \textgreater \ 0\\\\
f'(x)=(x^x)'=x^x(1+\ln x)\\
\texttt{(Asta e o formula din tabelul de derivate)}\\\\
\texttt{In forma scrisa in enunt, derivata este:}\\\\
u(t)=t^t,~~~t\ \textgreater \ 0\\
u'(t)=(t^t)'=t^t(1+\ln t)
[/tex]
[tex]\displaystyle \bf \\
\text{O formula mai generala din care o putem deduce pe asta, este:}\\\\
f(x)=u^v,~~u\ \textgreater \ 0,\texttt{unde u si v sunt functii:}\\\\
f'(x)=(u^v)'=u^v\left[\frac{u'}{u}\cdot v+v'\ln u\right]\\\\
\texttt{Daca facem inlocuirile: }u(x)=x~~\texttt{ si }~~v(x)=x\\
\texttt{obtinem formula de mai sus.}[/tex]