(((1+e^x)/2)^9)^'

解

((\frac{1 + e ^{x}}{2})^{9})^{^{'}}

\frac{9 e ^{x} ( 1 + e ^{x} ) ^{8}}{512}

解答ステップ

((\frac{1 + e ^{x}}{2})^{9})^{'}

連鎖法則を適用:

9 (\frac{1 + e ^{x}}{2})^{8} (\frac{1 + e ^{x}}{2})^{'}

= 9 (\frac{1 + e ^{x}}{2})^{8} (\frac{1 + e ^{x}}{2})^{'}

(\frac{1 + e ^{x}}{2})^{'} = \frac{1}{2} e^{x}

= 9 (\frac{1 + e ^{x}}{2})^{8} \frac{1}{2} e^{x}

簡素化

9 (\frac{1 + e ^{x}}{2})^{8} \frac{1}{2} e^{x} : \frac{9 e ^{x} ( 1 + e ^{x} ) ^{8}}{512}

= \frac{9 e ^{x} ( 1 + e ^{x} ) ^{8}}{512}