What is the derivative of 1/(sqrt(2pi)e^{-(x^2)/2}) ?

The derivative of 1/(sqrt(2pi)e^{-(x^2)/2}) is -(e^{-(x^2)/2}x)/(2^{1/2)pi^{1/2}}

What is the first derivative of 1/(sqrt(2pi)e^{-(x^2)/2}) ?

The first derivative of 1/(sqrt(2pi)e^{-(x^2)/2}) is -(e^{-(x^2)/2}x)/(2^{1/2)pi^{1/2}}

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\frac{d}{d x} (\frac{1}{2 π} e^{- \frac{x ^{2}}{2}})

- \frac{e ^{- \frac{x ^{2}}{2}} x}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{2 π} e^{- \frac{x ^{2}}{2}})

Simplify

\frac{1}{2 π} e^{- \frac{x ^{2}}{2}} : \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}} e^{- \frac{x ^{2}}{2}}

= \frac{d}{d x} (\frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}} e^{- \frac{x ^{2}}{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{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

= \frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}} e^{- \frac{x ^{2}}{2}} (- x)

Simplify

\frac{1}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}} e^{- \frac{x ^{2}}{2}} (- x) : - \frac{e ^{- \frac{x ^{2}}{2}} x}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}}

= - \frac{e ^{- \frac{x ^{2}}{2}} x}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}}

\frac{d}{d x} (A x^{2} e^{x} + B x e^{x} + C e^{x})

\int \frac{1}{10 x} d x

d er i v a t i v e y^{2}

f^{^{'}} (x) = 3 arctan (x^{2} - 3 x + 2)

\int \frac{sin ( 2 x )}{cos ^{3} ( 2 x )} d x

What is the derivative of 1/(sqrt(2pi)e^{-(x^2)/2}) ?
The derivative of 1/(sqrt(2pi)e^{-(x^2)/2}) is -(e^{-(x^2)/2}x)/(2^{1/2)pi^{1/2}}
What is the first derivative of 1/(sqrt(2pi)e^{-(x^2)/2}) ?
The first derivative of 1/(sqrt(2pi)e^{-(x^2)/2}) is -(e^{-(x^2)/2}x)/(2^{1/2)pi^{1/2}}