derivative p(t)=12te^{-t/6}

解答

导数

p (t) = 12 t e^{- \frac{t}{6}}

12 (e^{- \frac{t}{6}} - \frac{e ^{- \frac{t}{6}} t}{6})

求解步骤

\frac{d}{d t} (12 t e^{- \frac{t}{6}})

将常数提出:

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

= 12 \frac{d}{d t} (t e^{- \frac{t}{6}})

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t, g = e^{- \frac{t}{6}}

= 12 (\frac{d t}{d t} e^{- \frac{t}{6}} + \frac{d}{d t} (e^{- \frac{t}{6}}) t)

\frac{d t}{d t} = 1

\frac{d}{d t} (e^{- \frac{t}{6}}) = - \frac{1}{6} e^{- \frac{t}{6}}

= 12 (1 \cdot e^{- \frac{t}{6}} + (- \frac{1}{6} e^{- \frac{t}{6}}) t)

化简

12 (1 \cdot e^{- \frac{t}{6}} + (- \frac{1}{6} e^{- \frac{t}{6}}) t) : 12 (e^{- \frac{t}{6}} - \frac{e ^{- \frac{t}{6}} t}{6})

= 12 (e^{- \frac{t}{6}} - \frac{e ^{- \frac{t}{6}} t}{6})

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