derivative of-e^{-x^2}

解答

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

2 e^{- x^{2}} x

求解步骤

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

将常数提出:

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

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

使用连锁律:

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

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

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

= - e^{- x^{2}} (- 2 x)

化简

= 2 e^{- x^{2}} x

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