d/(dt)((4)(7+e^{-t^2}))

解答

\frac{d}{d t} ((4) (7 + e^{- t^{2}}))

- 8 e^{- t^{2}} t

求解步骤

\frac{d}{d t} ((4) (7 + e^{- t^{2}}))

将常数提出:

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

= 4 \frac{d}{d t} (7 + e^{- t^{2}})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 4 (\frac{d}{d t} (7) + \frac{d}{d t} (e^{- t^{2}}))

\frac{d}{d t} (7) = 0

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

= 4 (0 - 2 e^{- t^{2}} t)

化简

= - 8 e^{- t^{2}} t

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