What is the first d/(dt)(e^{at}) ?

The first d/(dt)(e^{at}) is e^{at}a

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d/(dt)(e^{at})

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

e^{a t} a

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d t} (a t) = a

= e^{a t} a

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