Derivative of exp(1/x)

The solution

You have entered [src]

 1
 -
 x
e

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

exp(1/x)

Detail solution

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

$- \frac{e^{\frac{1}{x}}}{x^{2}}$

The answer is:

$- \frac{e^{\frac{1}{x}}}{x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  1 
  - 
  x 
-e  
----
  2 
 x

$$- \frac{e^{\frac{1}{x}}}{x^{2}}$$

Simplify

The second derivative [src]

         1
         -
/    1\  x
|2 + -|*e 
\    x/   
----------
     3    
    x

$$\frac{\left(2 + \frac{1}{x}\right) e^{\frac{1}{x}}}{x^{3}}$$

Simplify

The third derivative [src]

               1 
               - 
 /    1    6\  x 
-|6 + -- + -|*e  
 |     2   x|    
 \    x     /    
-----------------
         4       
        x

$$- \frac{\left(6 + \frac{6}{x} + \frac{1}{x^{2}}\right) e^{\frac{1}{x}}}{x^{4}}$$

Simplify

The graph

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of exp(1/x)

The graph:

Piecewise:

The solution