詳解：(1) 等號兩邊取對數

\(\ln y = \ln {x^x}\quad  \Rightarrow \quad \ln y = x\ln x\)

(2) 等號兩邊微分

\(\frac{1}{y}y' = 1 \cdot \ln x + x \cdot \frac{1}{x}\quad  \Rightarrow \quad y' = y\left( {1 \cdot \ln x + x \cdot \frac{1}{x}} \right)\)

\( \Rightarrow y' = {x^x} \left( {\ln x + 1} \right)\)