What is the d/(dt)(4e^{-3t}) ?

The d/(dt)(4e^{-3t}) is -12e^{-3t}

What is the first d/(dt)(4e^{-3t}) ?

The first d/(dt)(4e^{-3t}) is -12e^{-3t}

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\frac{d}{d t} (4 e^{- 3 t})

- 12 e^{- 3 t}

Solution steps

\frac{d}{d t} (4 e^{- 3 t})

Take the constant out:

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

= 4 \frac{d}{d t} (e^{- 3 t})

Apply the chain rule:

e^{- 3 t} \frac{d}{d t} (- 3 t)

= e^{- 3 t} \frac{d}{d t} (- 3 t)

\frac{d}{d t} (- 3 t) = - 3

= 4 e^{- 3 t} (- 3)

Simplify

= - 12 e^{- 3 t}

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