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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (e^{4 x} + e^{- 4 x}) = e^{4 x} \cdot 4 - 4 e^{- 4 x}

\frac{d x}{d x} = 1

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

Simplify

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

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

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