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

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

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

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

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derivative of

5 e^{- x}

- 5 e^{- x}

Solution steps

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

Take the constant out:

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

= 5 \frac{d}{d x} (e^{- x})

Apply the chain rule:

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

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

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

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

Simplify

= - 5 e^{- x}

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