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

The derivative of 5e^{-5x} is -25e^{-5x}

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

The first derivative of 5e^{-5x} is -25e^{-5x}

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

- 25 e^{- 5 x}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

= - 25 e^{- 5 x}

What is the derivative of 5e^{-5x} ?
The derivative of 5e^{-5x} is -25e^{-5x}
What is the first derivative of 5e^{-5x} ?
The first derivative of 5e^{-5x} is -25e^{-5x}