derivative of ln(e^x-y)

解

\frac{d}{d x} (ln (e^{x} - y))

\frac{e ^{x} - \frac{d y}{d x}}{e ^{x} - y}

解答ステップ

\frac{d}{d x} (ln (e^{x} - y))

連鎖法則を適用:

\frac{1}{e ^{x} - y} \frac{d}{d x} (e^{x} - y)

= \frac{1}{e ^{x} - y} \frac{d}{d x} (e^{x} - y)

\frac{d}{d x} (e^{x} - y) = e^{x} - \frac{d y}{d x}

= \frac{1}{e ^{x} - y} (e^{x} - \frac{d y}{d x})

簡素化

\frac{1}{e ^{x} - y} (e^{x} - \frac{d y}{d x}) : \frac{e ^{x} - \frac{d y}{d x}}{e ^{x} - y}

= \frac{e ^{x} - \frac{d y}{d x}}{e ^{x} - y}