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exp^x^-2
The derivative of the function/ exp^x^-2

Derivative of exp^x^-2

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 1 
 --
  2
 x 
e
e1x2e^{\frac{1}{x^{2}}} 
  / 1 \
  | --|
  |  2|
d | x |
--\e  /
dx
ddxe1x2\frac{d}{d x} e^{\frac{1}{x^{2}}}
Transform
Detail solution

  1. Let u=1x2u = \frac{1}{x^{2}}.

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

  3. Then, apply the chain rule. Multiply by ddx1x2\frac{d}{d x} \frac{1}{x^{2}}:

    1. Apply the power rule: 1x2\frac{1}{x^{2}} goes to −2x3- \frac{2}{x^{3}}

    The result of the chain rule is:

    −2e1x2x3- \frac{2 e^{\frac{1}{x^{2}}}}{x^{3}}

The answer is:

−2e1x2x3- \frac{2 e^{\frac{1}{x^{2}}}}{x^{3}}

The graph
02468-8-6-4-2-1010-2e462e46
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    1 
    --
     2
    x 
-2*e  
------
   3  
  x
−2e1x2x3- \frac{2 e^{\frac{1}{x^{2}}}}{x^{3}}
Simplify
The second derivative [src] 
            1 
            --
             2
  /    2 \  x 
2*|3 + --|*e  
  |     2|    
  \    x /    
--------------
       4      
      x
2⋅(3+2x2)e1x2x4\frac{2 \cdot \left(3 + \frac{2}{x^{2}}\right) e^{\frac{1}{x^{2}}}}{x^{4}}
Simplify
The third derivative [src] 
                  1 
                  --
                   2
   /    2    9 \  x 
-4*|6 + -- + --|*e  
   |     4    2|    
   \    x    x /    
--------------------
          5         
         x
−4⋅(6+9x2+2x4)e1x2x5- \frac{4 \cdot \left(6 + \frac{9}{x^{2}} + \frac{2}{x^{4}}\right) e^{\frac{1}{x^{2}}}}{x^{5}}
Simplify
The graph
Derivative of exp^x^-2
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