What is the derivative of (e^{7x}+e^{-7x}/x) ?

The derivative of (e^{7x}+e^{-7x}/x) is (7e^{7x}x-7e^{-7x}x-e^{7x}-e^{-7x})/(x^2)

What is the first derivative of (e^{7x}+e^{-7x}/x) ?

The first derivative of (e^{7x}+e^{-7x}/x) is (7e^{7x}x-7e^{-7x}x-e^{7x}-e^{-7x})/(x^2)

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Popular >

\frac{d}{d x} (\frac{e ^{7 x} + e ^{- 7 x}}{x})

\frac{7 e ^{7 x} x - 7 e ^{- 7 x} x - e ^{7 x} - e ^{- 7 x}}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{7 x} + e ^{- 7 x}}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{7 x} + e ^{- 7 x} ) x - \frac{d x}{d x} ( e ^{7 x} + e ^{- 7 x} )}{x ^{2}}

\frac{d}{d x} (e^{7 x} + e^{- 7 x}) = e^{7 x} \cdot 7 - 7 e^{- 7 x}

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

= \frac{( e ^{7 x} \cdot 7 - 7 e ^{- 7 x} ) x - 1 \cdot ( e ^{7 x} + e ^{- 7 x} )}{x ^{2}}

Simplify

\frac{( e ^{7 x} \cdot 7 - 7 e ^{- 7 x} ) x - 1 \cdot ( e ^{7 x} + e ^{- 7 x} )}{x ^{2}} : \frac{7 e ^{7 x} x - 7 e ^{- 7 x} x - e ^{7 x} - e ^{- 7 x}}{x ^{2}}

= \frac{7 e ^{7 x} x - 7 e ^{- 7 x} x - e ^{7 x} - e ^{- 7 x}}{x ^{2}}

\int_{0}^{1} - x^{2} d x

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

2 e^{- 3 t}

\int 17 x^{2} sin (π x) d x

\int - x + 1 d x

What is the derivative of (e^{7x}+e^{-7x}/x) ?
The derivative of (e^{7x}+e^{-7x}/x) is (7e^{7x}x-7e^{-7x}x-e^{7x}-e^{-7x})/(x^2)
What is the first derivative of (e^{7x}+e^{-7x}/x) ?
The first derivative of (e^{7x}+e^{-7x}/x) is (7e^{7x}x-7e^{-7x}x-e^{7x}-e^{-7x})/(x^2)