derivative (m+2)/(m^2+5m+6)

解

導関数

\frac{m + 2}{m ^{2} + 5 m + 6}

\frac{- m ^{2} - 4 m - 4}{( m ^{2} + 5 m + 6 ) ^{2}}

解答ステップ

\frac{d}{d m} (\frac{m + 2}{m ^{2} + 5 m + 6})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d m} ( m + 2 ) ( m ^{2} + 5 m + 6 ) - \frac{d}{d m} ( m ^{2} + 5 m + 6 ) ( m + 2 )}{( m ^{2} + 5 m + 6 ) ^{2}}

\frac{d}{d m} (m + 2) = 1

\frac{d}{d m} (m^{2} + 5 m + 6) = 2 m + 5

= \frac{1 \cdot ( m ^{2} + 5 m + 6 ) - ( 2 m + 5 ) ( m + 2 )}{( m ^{2} + 5 m + 6 ) ^{2}}

簡素化

\frac{1 \cdot ( m ^{2} + 5 m + 6 ) - ( 2 m + 5 ) ( m + 2 )}{( m ^{2} + 5 m + 6 ) ^{2}} : \frac{- m ^{2} - 4 m - 4}{( m ^{2} + 5 m + 6 ) ^{2}}

= \frac{- m ^{2} - 4 m - 4}{( m ^{2} + 5 m + 6 ) ^{2}}