(\partial)/(\partial x)((ln(1+e^{(x)}))^2)

解

\frac{\partial}{\partial x} ((ln (1 + e^{(x)}))^{2})

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

解答ステップ

\frac{\partial}{\partial x} ((ln (1 + e^{(x)}))^{2})

連鎖法則を適用:

2 ln (1 + e^{x}) \frac{\partial}{\partial x} (ln (1 + e^{x}))

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

\frac{\partial}{\partial x} (ln (1 + e^{x})) = \frac{e ^{x}}{1 + e ^{x}}

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

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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