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{( 5 x ^{2} )}{1 - 5 x ^{3}} d x

x \to 0 + lim (sin (\frac{π}{x}))

\frac{\partial}{\partial x} (y - x^{2})

2 x^{2} y^{^{'}} = y^{^{'}} + 6 x e^{(- y)}

\int \frac{2}{3} t^{\frac{3}{2}} - 2 sin (t) + C d t

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}