Mister Exam

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The derivative of the function/ e^-t

Derivative of e^-t

The solution

You have entered [src]

 -t
E

$$e^{- t}$$

E^(-t)

Detail solution

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

$- e^{- t}$

The answer is:

$- e^{- t}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  -t
-e

$$- e^{- t}$$

Simplify

The second derivative [src]

 -t
e

$$e^{- t}$$

Simplify

The third derivative [src]

  -t
-e

$$- e^{- t}$$

Simplify

The graph

Derivative of e^-t