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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial y} (ln (x - 8 y))

x \to 6 lim (5)

x^{2} - 25, 25 - x^{2}

\frac{3}{2} x^{2}

n = 3 \sum \infty \frac{n}{n + 2}

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