詳解：換底公式

\(f(x) = {\log _7}({x^2} + 2x + 3){\rm{ = }}\frac{{\ln ({x^2} + 2x + 3)}}{{\ln 7}}\)

\(f'(x) = \frac{{{{\left[ {\ln ({x^2} + 2x + 3)} \right]}^\prime }}}{{\ln 7}} = \frac{1}{{\ln 7}} \cdot \frac{1}{{{x^2} + 2x + 3}} \cdot (2x + 2)\)