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

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

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

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

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derivative

- e^{- x}

Solution steps

\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

= e^{- x} (- 1)

Simplify

= - e^{- x}

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