対数微分法
もとの関数の導関数を得るために整理すると
f ′ ( x ) = ∏ i ( f i ( x ) ) α i ( x ) ⏞ f ( x ) × ∑ i { α i ′ ( x ) ⋅ ln  ( f i ( x ) ) + α i ( x ) ⋅ f i ′ ( x ) f i ( x ) } ⏞ [ ln  ( f ( x ) ) ] ′ {\displaystyle f'(x)=\overbrace {\prod _{i}(f_{i}(x))^{\alpha _{i}(x)}} ^{f(x)}\times \overbrace {\sum _{i}\left\{\alpha _{i}'(x)\cdot \ln(f_{i}(x))+\alpha _{i}(x)\cdot {\frac {f_{i}'(x)}{f_{i}(x)}}\right\}} ^{[\ln(f(x))]'}}