What is the derivative of e^{(-y^2)/2} ?

The derivative of e^{(-y^2)/2} is -e^{-(y^2)/2}y

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

The first derivative of e^{(-y^2)/2} is -e^{-(y^2)/2}y

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derivative of

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

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

Solution steps

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

Simplify

e^{\frac{- y ^{2}}{2}} : e^{- \frac{y ^{2}}{2}}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (x^{5} tan (x))

n = 1 \sum \infty \frac{1}{n 3 ^{n}} x^{n}

\frac{d y}{d x} = e^{3 x + 2 y}

t^{2} y^{^{''}} + 3 t y^{^{'}} - 24 y = 0

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