What is (\partial)/(\partial t)(e^{-t}) ?

The answer to (\partial)/(\partial t)(e^{-t}) is -e^{-t}

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(\partial)/(\partial t)(e^{-t})

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

- e^{- t}

Solution steps

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

Apply the chain rule:

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

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

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

= e^{- t} (- 1)

Simplify

= - e^{- t}

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What is (\partial)/(\partial t)(e^{-t}) ?
The answer to (\partial)/(\partial t)(e^{-t}) is -e^{-t}