d/(dt)((x)(5t+e^{-t}))

解答

\frac{d}{d t} ((x) (5 t + e^{- t}))

x (5 - e^{- t})

求解步骤

\frac{d}{d t} ((x) (5 t + e^{- t}))

将

x

视为常数

将常数提出:

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

= x \frac{d}{d t} (5 t + e^{- t})

使用微分加减法定则:

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

= x (\frac{d}{d t} (5 t) + \frac{d}{d t} (e^{- t}))

\frac{d}{d t} (5 t) = 5

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

= x (5 - e^{- t})

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