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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

X X + 1

\int \frac{t - 3}{t} d t

\frac{\partial}{\partial x} (y x - y^{2} - x + 3 y)

(9 x + 8) x^{2}

\int_{0}^{\infty} \frac{y e ^{\frac{- y}{a}}}{a} d y

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