derivative ((2-z)^{2/3})/(4z+5)

解

導関数

\frac{( 2 - z ) ^{\frac{2}{3}}}{4 z + 5}

\frac{4 z - 34}{3 ( 4 z + 5 ) ^{2} ( 2 - z ) ^{\frac{1}{3}}}

解答ステップ

\frac{d}{d z} (\frac{( 2 - z ) ^{\frac{2}{3}}}{4 z + 5})

商の法則を適用:

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

= \frac{\frac{d}{d z} ( ( 2 - z ) ^{\frac{2}{3}} ) ( 4 z + 5 ) - \frac{d}{d z} ( 4 z + 5 ) ( 2 - z ) ^{\frac{2}{3}}}{( 4 z + 5 ) ^{2}}

\frac{d}{d z} ((2 - z)^{\frac{2}{3}}) = - \frac{2}{3 ( 2 - z ) ^{\frac{1}{3}}}

\frac{d}{d z} (4 z + 5) = 4

= \frac{( - \frac{2}{3 ( 2 - z ) ^{\frac{1}{3}}} ) ( 4 z + 5 ) - 4 ( 2 - z ) ^{\frac{2}{3}}}{( 4 z + 5 ) ^{2}}

簡素化

\frac{( - \frac{2}{3 ( 2 - z ) ^{\frac{1}{3}}} ) ( 4 z + 5 ) - 4 ( 2 - z ) ^{\frac{2}{3}}}{( 4 z + 5 ) ^{2}} : \frac{4 z - 34}{3 ( 4 z + 5 ) ^{2} ( 2 - z ) ^{\frac{1}{3}}}

= \frac{4 z - 34}{3 ( 4 z + 5 ) ^{2} ( 2 - z ) ^{\frac{1}{3}}}