"What is the derivative of e−x?" was answered by our experts

Russell Gillen

Answered question

2021-12-21

What is the derivative of

e^{- x}

braodagxj

Beginner2021-12-22Added 38 answers

\frac{d y}{d x} = - e^{- x}

As,

y = e^{- x}

Let,

y = e^{u}

, and u=-x

∴ \frac{d y}{d u} = e^{u}

and

\frac{d u}{d x} = - 1

\frac{d y}{d x} = \frac{d y}{d u} \times \frac{d u}{d x}

∴ \frac{d y}{d x} = e^{u} \times (- 1) = - e^{u}

Substitute u=-x

∴ \frac{d y}{d x} = - e^{- x}

Travis Hicks

Beginner2021-12-23Added 29 answers

We can use the chain rule:
If y=f(g(x)), then

\frac{d y}{d x} = f^{'} (g (x)) \times g^{'} (x)

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

RizerMix

Expert2021-12-29Added 656 answers

$\frac{d y}{d x} = - e^{- x}$

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