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

解答

\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}}}

求解步骤

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

化简

\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}})

将常数提出:

(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}})

使用连锁律:

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)

化简

\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}}}

x \to 3 lim (\frac{x - 3}{x + 3})

x y^{^{'}} + 4 y = - 3 x

\int - \frac{x}{x ^{2} + 4} d x

\int \frac{- 4 x + 10}{x ^{3}} d x

l a pl a ce t r an s f or m {0}