derivative (1/(2x+3))^3

解

導関数

(\frac{1}{2 x + 3})^{3}

- \frac{6}{( 2 x + 3 ) ^{4}}

解答ステップ

\frac{d}{d x} ((\frac{1}{2 x + 3})^{3})

連鎖法則を適用:

3 (\frac{1}{2 x + 3})^{2} \frac{d}{d x} (\frac{1}{2 x + 3})

= 3 (\frac{1}{2 x + 3})^{2} \frac{d}{d x} (\frac{1}{2 x + 3})

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

= 3 (\frac{1}{2 x + 3})^{2} (- \frac{2}{( 2 x + 3 ) ^{2}})

簡素化

3 (\frac{1}{2 x + 3})^{2} (- \frac{2}{( 2 x + 3 ) ^{2}}) : - \frac{6}{( 2 x + 3 ) ^{4}}

= - \frac{6}{( 2 x + 3 ) ^{4}}