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

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derivative of

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

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

Solution steps

\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

\frac{d}{d x} ((4 x^{3} + 3)^{2})

x \to - 2 lim (3 x^{2} - 5 x + 7)

(- 3, 5), (6, - 1)

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

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