What is the derivative of f(x)=e^{-3x} ?

The derivative of f(x)=e^{-3x} is -3e^{-3x}

What is the first derivative of f(x)=e^{-3x} ?

The first derivative of f(x)=e^{-3x} is -3e^{-3x}

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derivative

- 3 e^{- 3 x}

Solution steps

\frac{d}{d x} (e^{- 3 x})

Apply the chain rule:

e^{- 3 x} \frac{d}{d x} (- 3 x)

= e^{- 3 x} \frac{d}{d x} (- 3 x)

\frac{d}{d x} (- 3 x) = - 3

= e^{- 3 x} (- 3)

Simplify

= - 3 e^{- 3 x}

What is the derivative of f(x)=e^{-3x} ?
The derivative of f(x)=e^{-3x} is -3e^{-3x}
What is the first derivative of f(x)=e^{-3x} ?
The first derivative of f(x)=e^{-3x} is -3e^{-3x}