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

The derivative of ((e^x-2)/((1-e^{-x))^2}) is (e^{-x}(-3e^x+e^{2x}+4))/((1-e^{-x))^3}

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

The first derivative of ((e^x-2)/((1-e^{-x))^2}) is (e^{-x}(-3e^x+e^{2x}+4))/((1-e^{-x))^3}

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

\frac{e ^{- x} ( - 3 e ^{x} + e ^{2 x} + 4 )}{( 1 - e ^{- x} ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{e ^{x} ( 1 - e ^{- x} ) ^{2} - 2 ( 1 - e ^{- x} ) e ^{- x} ( e ^{x} - 2 )}{( ( 1 - e ^{- x} ) ^{2} ) ^{2}} : \frac{e ^{- x} ( - 3 e ^{x} + e ^{2 x} + 4 )}{( 1 - e ^{- x} ) ^{3}}

= \frac{e ^{- x} ( - 3 e ^{x} + e ^{2 x} + 4 )}{( 1 - e ^{- x} ) ^{3}}

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

\frac{\partial}{\partial x} (5 x y)

\frac{d}{d x} ((e^{- x} - e^{5}) (e^{x} + e^{- 3}))

\frac{d}{d x} (2^{2 x + 1})

y = \frac{1}{x - 2}, at x = 4

What is the derivative of ((e^x-2)/((1-e^{-x))^2}) ?
The derivative of ((e^x-2)/((1-e^{-x))^2}) is (e^{-x}(-3e^x+e^{2x}+4))/((1-e^{-x))^3}
What is the first derivative of ((e^x-2)/((1-e^{-x))^2}) ?
The first derivative of ((e^x-2)/((1-e^{-x))^2}) is (e^{-x}(-3e^x+e^{2x}+4))/((1-e^{-x))^3}