Evaluate
\left\{\begin{matrix}\frac{a^{a}-1}{\ln(a)},&a>0\text{ and }a\neq 1\\a,&a=1\end{matrix}\right.
Differentiate w.r.t. a
\left\{\begin{matrix}-\frac{a^{a-1}}{\ln(a)^{2}}+\frac{a^{a}}{\ln(a)}+\frac{1}{a\ln(a)^{2}}+a^{a},&a>0\text{ and }a\neq 1\\1,&a=1\end{matrix}\right.
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