Derivative of 1/e^x

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1 
--
 x
E

$$\frac{1}{e^{x}}$$

1/(E^x)

Detail solution

Let $u = e^{x}$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} e^{x}$ :
1. The derivative of $e^{x}$ is itself.
The result of the chain rule is:

$- e^{- x}$

The answer is:

$- e^{- x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  -x
-e

$$- e^{- x}$$

Simplify

The second derivative [src]

 -x
e

$$e^{- x}$$

Simplify

The third derivative [src]

  -x
-e

$$- e^{- x}$$

Simplify

The graph