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}}

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)