What is the derivative of 5e^{-t} ?

The derivative of 5e^{-t} is -5e^{-t}

What is the first derivative of 5e^{-t} ?

The first derivative of 5e^{-t} is -5e^{-t}

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derivative of

5 e^{- t}

- 5 e^{- t}

Solution steps

\frac{d}{d t} (5 e^{- t})

Take the constant out:

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

= 5 \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

= 5 e^{- t} (- 1)

Simplify

= - 5 e^{- t}

What is the derivative of 5e^{-t} ?
The derivative of 5e^{-t} is -5e^{-t}
What is the first derivative of 5e^{-t} ?
The first derivative of 5e^{-t} is -5e^{-t}