What is the derivative of p(t)=12te^{-t/6} ?

The derivative of p(t)=12te^{-t/6} is 12(e^{-t/6}-(e^{-t/6}t)/6)

What is the first derivative of p(t)=12te^{-t/6} ?

The first derivative of p(t)=12te^{-t/6} is 12(e^{-t/6}-(e^{-t/6}t)/6)

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

(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)

Simplify

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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What is the derivative of p(t)=12te^{-t/6} ?
The derivative of p(t)=12te^{-t/6} is 12(e^{-t/6}-(e^{-t/6}t)/6)
What is the first derivative of p(t)=12te^{-t/6} ?
The first derivative of p(t)=12te^{-t/6} is 12(e^{-t/6}-(e^{-t/6}t)/6)