derivative of 1/(1-e^x)

解答

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

\frac{e ^{x}}{( 1 - e ^{x} ) ^{2}}

求解步骤

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

使用指数法则:

\frac{1}{a} = a^{- 1}

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

使用连锁律:

- \frac{1}{( 1 - e ^{x} ) ^{2}} \frac{d}{d x} (1 - e^{x})

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

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

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

化简

- \frac{1}{( 1 - e ^{x} ) ^{2}} (- e^{x}) : \frac{e ^{x}}{( 1 - e ^{x} ) ^{2}}

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

x \to - 1 + lim (x + 1)

\int 2 x^{1} e^{- y}

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h \to 0 lim (\frac{( 1 + h ) - 1}{h})