derivative f(x)=7e^{-x^2}

解答

导数

f (x) = 7 e^{- x^{2}}

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

求解步骤

\frac{d}{d x} (7 e^{- x^{2}})

将常数提出:

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

= 7 \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

= 7 e^{- x^{2}} (- 2 x)

化简

= - 14 e^{- x^{2}} x

a re a x^{2} + 2 x, x + 2, - 2, 1

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