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

Derivative of e^(1/x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
x ___
\/ E
e1xe^{\frac{1}{x}} 
E^(1/x)
Detail solution

  1. Let u=1xu = \frac{1}{x}.

  2. The derivative of eue^{u} is itself.

  3. Then, apply the chain rule. Multiply by ddx1x\frac{d}{d x} \frac{1}{x}:

    1. Apply the power rule: 1x\frac{1}{x} goes to −1x2- \frac{1}{x^{2}}

    The result of the chain rule is:

    −e1xx2- \frac{e^{\frac{1}{x}}}{x^{2}}

The answer is:

−e1xx2- \frac{e^{\frac{1}{x}}}{x^{2}}

The graph
02468-8-6-4-2-1010-20000002000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1 
  - 
  x 
-e  
----
  2 
 x
−e1xx2- \frac{e^{\frac{1}{x}}}{x^{2}}
Simplify
The second derivative [src] 
         1
         -
/    1\  x
|2 + -|*e 
\    x/   
----------
     3    
    x
(2+1x)e1xx3\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
−(6+6x+1x2)e1xx4- \frac{\left(6 + \frac{6}{x} + \frac{1}{x^{2}}\right) e^{\frac{1}{x}}}{x^{4}}
Simplify
The graph
Derivative of e^(1/x)
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