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}}

\int - \frac{x}{x ^{2} + y ^{2}} d x

y^{^{'}} + \frac{y}{t} = 2 e^{t}

x^{2} + 6 x

y^{^{'}} = \frac{2}{3 x} y + \frac{2 x}{y}

y = x^{2} - 5 x, (7, 14)

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}