Mister Exam

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The derivative of the function/ e^-x

Derivative of e^-x

The solution

You have entered [src]

 -x
e

$$e^{- x}$$

d / -x\
--\e  /
dx

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

Transform

Detail solution

Let $u = - x$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- x\right)$ :
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x$ goes to $1$
  So, the result is: $-1$
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

Derivative of e^-x