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

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

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

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

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

e^{- ∣ x ∣}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (∣ x ∣) = \frac{x}{∣ x ∣}

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

Simplify

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

= e^{- ∣ x ∣}

\frac{\partial}{\partial x} (2 t^{2} + 2 x)

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

4 x^{2} - 2 x - 1

y^{^{'}} = e^{y}

x \to 2 lim (\frac{x + 1}{2 - x})

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