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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derivative of

\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}}

\int \frac{y}{16 - 9 y ^{4}} d y

\int (2 x^{3} + x) (x^{4} + x^{2}) d x

f (x) = - 2 x + 7

\int 7 x^{9} - 3 x^{6} + 10 x^{3} d x

\int \frac{1}{( x + 1 ) ^{5}} d x

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}