詳解：利用連鎖率

\(f'(x) = {{\rm{3}}^{{3^x}}}({3^x})'ln{\rm{3 = }}{{\rm{3}}^{{3^x}}}({3^x})ln3 \cdot ln{\rm{3 = }}{{\rm{3}}^{{3^x}}}({3^x}){\left( {ln3} \right)^2}\)

或設 \(y = {{\rm{3}}^{{3^x}}}\quad  \Rightarrow \quad \ln y = {3^x}\ln 3\)

等號兩邊同時微分

\(\frac{{\rm{1}}}{y}y' = {3^x}ln3 \cdot \ln 3\quad  \Rightarrow \quad y' = y \cdot {3^x}ln3 \cdot \ln 3 = {{\rm{3}}^{{3^x}}}{3^x}{\left( {ln3} \right)^2}\)