# What is the derivative of e^(-x)?

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#### Explanation

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#### Explanation:

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May 31, 2016

$- {e}^{-} x$ is derivative of ${e}^{-} x$

#### Explanation:

$f \left(x\right) = {e}^{-} x$

differentiating on both sides

$f ' \left(x\right) = {e}^{-} x \cdot - 1$

differentiation of ${e}^{-} x = {e}^{-} x \cdot - 1$ since differentiation of ${e}^{x} = {e}^{x}$, but the derivative of $- x$ by applying the chain rule is $- 1$.

Therefore $f ' \left(x\right) = - {e}^{-} x$.

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