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

The d/(dt)(Ae^{-t}) is -Ae^{-t}

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

The first d/(dt)(Ae^{-t}) is -Ae^{-t}

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

- A e^{- t}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d t} (- t) = - 1

= A e^{- t} (- 1)

Simplify

= - A e^{- t}

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