What is the derivative of-e^{-4x} ?

The derivative of-e^{-4x} is 4e^{-4x}

What is the first derivative of-e^{-4x} ?

The first derivative of-e^{-4x} is 4e^{-4x}

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\frac{d}{d x} (- e^{- 4 x})

4 e^{- 4 x}

Solution steps

\frac{d}{d x} (- e^{- 4 x})

Take the constant out:

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

= - \frac{d}{d x} (e^{- 4 x})

Apply the chain rule:

e^{- 4 x} \frac{d}{d x} (- 4 x)

= e^{- 4 x} \frac{d}{d x} (- 4 x)

\frac{d}{d x} (- 4 x) = - 4

= - e^{- 4 x} (- 4)

Simplify

= 4 e^{- 4 x}

What is the derivative of-e^{-4x} ?
The derivative of-e^{-4x} is 4e^{-4x}
What is the first derivative of-e^{-4x} ?
The first derivative of-e^{-4x} is 4e^{-4x}