en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of e^{-a|x|}

Solution

\frac{d}{d x} (e^{- a ∣ x ∣})

Solution

- \frac{a e ^{- a ∣ x ∣} x}{∣ x ∣}

Solution steps

\frac{d}{d x} (e^{- a ∣ x ∣})

Apply the chain rule:

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

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

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

= e^{- a ∣ x ∣} (- \frac{a x}{∣ x ∣})

Simplify

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

= - \frac{a e ^{- a ∣ x ∣} x}{∣ x ∣}

Popular Examples

integral of (2x)/((x^2+1)^{90)}

\int \frac{2 x}{( x ^{2} + 1 ) ^{90}} d x

derivative of f(8)=2(x-5)derivative of

f (8) = 2 (x - 5)

limit as h approaches c of h^3+4h^2-3

h \to c lim (h^{3} + 4 h^{2} - 3)

derivative of (x^3/3+3x^2-7x)

\frac{d}{d x} (\frac{x ^{3}}{3} + 3 x^{2} - 7 x)

taylor 5x^3+2x^2+6x+10 taylor

5 x^{3} + 2 x^{2} + 6 x + 10

Frequently Asked Questions (FAQ)

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