What is the d/(dt)(8te^{-t}) ?

The d/(dt)(8te^{-t}) is 8(e^{-t}-e^{-t}t)

What is the first d/(dt)(8te^{-t}) ?

The first d/(dt)(8te^{-t}) is 8(e^{-t}-e^{-t}t)

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\frac{d}{d t} (8 t e^{- t})

8 (e^{- t} - e^{- t} t)

Solution steps

\frac{d}{d t} (8 t e^{- t})

Take the constant out:

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

= 8 \frac{d}{d t} (t e^{- t})

Apply the Product Rule:

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

f = t, g = e^{- t}

= 8 (\frac{d t}{d t} e^{- t} + \frac{d}{d t} (e^{- t}) t)

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

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

= 8 (1 \cdot e^{- t} + (- e^{- t}) t)

Simplify

= 8 (e^{- t} - e^{- t} t)

What is the d/(dt)(8te^{-t}) ?
The d/(dt)(8te^{-t}) is 8(e^{-t}-e^{-t}t)
What is the first d/(dt)(8te^{-t}) ?
The first d/(dt)(8te^{-t}) is 8(e^{-t}-e^{-t}t)