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The derivative of the function/ e^(x-1)

Derivative of e^(x-1)

The solution

You have entered [src]

 x - 1
E

$$e^{x - 1}$$

E^(x - 1)

Detail solution

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

$e^{x - 1}$
Now simplify:

$e^{x - 1}$

The answer is:

$e^{x - 1}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 x - 1
E

$$e^{x - 1}$$

Simplify

The second derivative [src]

 -1 + x
e

$$e^{x - 1}$$

Simplify

The third derivative [src]

 -1 + x
e

$$e^{x - 1}$$

Simplify

The graph

Derivative of e^(x-1)