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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\frac{d ^{3}}{d x ^{3}} (x^{2} sin (x))

\frac{d}{d x} ((a - x)^{2})

\frac{d}{d x} (\frac{x ^{5}}{a + b} - \frac{x ^{2}}{a - b})

\frac{d}{d x} (0.7 x^{2})

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

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