en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

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

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

Popular Examples

integral of 1/(sqrt(16-t^2))

\int \frac{1}{16 - t ^{2}} d t

derivative of f(x)=ln(1+x)derivative of

f (x) = ln (1 + x)

derivative of ln((sqrt(2x)/(sin(x))))

\frac{d}{d x} (ln (\frac{2 x}{sin ( x )}))

derivative of y= 3/(sin(2x))derivative of

y = \frac{3}{sin ( 2 x )}

limit as x approaches 1 of ((x+3))/2

x \to 1 lim (\frac{( x + 3 )}{2})

Frequently Asked Questions (FAQ)

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