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

The derivative of f(x)=e^{-(x^2)/2} is -e^{-(x^2)/2}x

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

The first derivative of f(x)=e^{-(x^2)/2} is -e^{-(x^2)/2}x

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derivative of

f (x) = 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

\int_{2}^{8} (- x + 10) d x

y d x + (1 + x) d y = 0, y (0) = 1

\int (\frac{7}{x ^{5}} + 8 e^{2 x} - 4 x) d x

n = 1 \sum \infty \frac{- 2 ^{n}}{n ^{7}}

\frac{d}{d x} (\frac{12 - 3 y - 2 x}{4})

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