What is the derivative of e^{-t} ?

The derivative of e^{-t} is -e^{-t}

What is the first derivative of e^{-t} ?

The first derivative of e^{-t} is -e^{-t}

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derivative

- e^{- t}

Solution steps

\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

= e^{- t} (- 1)

Simplify

= - e^{- t}

What is the derivative of e^{-t} ?
The derivative of e^{-t} is -e^{-t}
What is the first derivative of e^{-t} ?
The first derivative of e^{-t} is -e^{-t}