What is the derivative of f(x)=e^{-5x} ?

The derivative of f(x)=e^{-5x} is -5e^{-5x}

What is the first derivative of f(x)=e^{-5x} ?

The first derivative of f(x)=e^{-5x} is -5e^{-5x}

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derivative of

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

- 5 e^{- 5 x}

Solution steps

\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

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

Simplify

= - 5 e^{- 5 x}

What is the derivative of f(x)=e^{-5x} ?
The derivative of f(x)=e^{-5x} is -5e^{-5x}
What is the first derivative of f(x)=e^{-5x} ?
The first derivative of f(x)=e^{-5x} is -5e^{-5x}