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Identical expressions
exp^(one /x)- one
exponent of to the power of (1 divide by x) minus 1
exponent of to the power of (one divide by x) minus one
exp(1/x)-1
exp1/x-1
exp^1/x-1
exp^(1 divide by x)-1
Similar expressions
exp^(1/x)+1

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

Derivative of exp^(1/x)-1

The solution

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x ___    
\/ E  - 1

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

E^(1/x) - 1

Detail solution

Differentiate $e^{\frac{1}{x}} - 1$ term by term:
1. Let $u = \frac{1}{x}$ .
2. The derivative of $e^{u}$ is itself.
3. 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:
  
  $- \frac{e^{\frac{1}{x}}}{x^{2}}$
4. The derivative of the constant $-1$ is zero.
The result 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

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Derivative of exp^(1/x)-1

The graph:

Piecewise:

The solution