What is the derivative of 1/(1-e^{-x}) ?

The derivative of 1/(1-e^{-x}) is -(e^{-x})/((1-e^{-x))^2}

What is the first derivative of 1/(1-e^{-x}) ?

The first derivative of 1/(1-e^{-x}) is -(e^{-x})/((1-e^{-x))^2}

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

- \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}

Simplify

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

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

\int e cos (x) d x

\frac{d}{d y} (\frac{a x + b y}{c x + d y})

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

\int \frac{x ^{2}}{7 - x} d x

n = 0 \sum \infty (\frac{x}{7})^{n}

What is the derivative of 1/(1-e^{-x}) ?
The derivative of 1/(1-e^{-x}) is -(e^{-x})/((1-e^{-x))^2}
What is the first derivative of 1/(1-e^{-x}) ?
The first derivative of 1/(1-e^{-x}) is -(e^{-x})/((1-e^{-x))^2}