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Popular >

derivative of e^{-|x|}

Solution

\frac{d}{d x} (e^{- ∣ x ∣})

Solution

- \frac{e ^{- ∣ x ∣} x}{∣ x ∣}

Solution steps

\frac{d}{d x} (e^{- ∣ x ∣})

Apply the chain rule:

e^{- ∣ x ∣} \frac{d}{d x} (- ∣ x ∣)

= e^{- ∣ x ∣} \frac{d}{d x} (- ∣ x ∣)

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

= e^{- ∣ x ∣} (- \frac{x}{∣ x ∣})

Simplify

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

= - \frac{e ^{- ∣ x ∣} x}{∣ x ∣}

Popular Examples

limit as x approaches-2 of (x+2)/(2x+4)

x \to - 2 lim (\frac{x + 2}{2 x + 4})

integral of 1/((x^2-1)^{3/2)}

\int \frac{1}{( x ^{2} - 1 ) ^{\frac{3}{2}}} d x

area y=4x^2-1,y=1-4x^2 area

y = 4 x^{2} - 1, y = 1 - 4 x^{2}

y^{'} = y (2 - y)

limit as x approaches 0 of 2x-x^2

x \to 0 lim (2 x - x^{2})

Frequently Asked Questions (FAQ)

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