Derivative of exp^x^-2

The solution

You have entered [src]

 1 
 --
  2
 x 
e

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

  / 1 \
  | --|
  |  2|
d | x |
--\e  /
dx

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

Transform

Detail solution

Let $u = \frac{1}{x^{2}}$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} \frac{1}{x^{2}}$ :
1. Apply the power rule: $\frac{1}{x^{2}}$ goes to $- \frac{2}{x^{3}}$
The result of the chain rule is:

$- \frac{2 e^{\frac{1}{x^{2}}}}{x^{3}}$

The answer is:

$- \frac{2 e^{\frac{1}{x^{2}}}}{x^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    1 
    --
     2
    x 
-2*e  
------
   3  
  x

$$- \frac{2 e^{\frac{1}{x^{2}}}}{x^{3}}$$

Simplify

The second derivative [src]

            1 
            --
             2
  /    2 \  x 
2*|3 + --|*e  
  |     2|    
  \    x /    
--------------
       4      
      x

$$\frac{2 \cdot \left(3 + \frac{2}{x^{2}}\right) e^{\frac{1}{x^{2}}}}{x^{4}}$$

Simplify

The third derivative [src]

                  1 
                  --
                   2
   /    2    9 \  x 
-4*|6 + -- + --|*e  
   |     4    2|    
   \    x    x /    
--------------------
          5         
         x

$$- \frac{4 \cdot \left(6 + \frac{9}{x^{2}} + \frac{2}{x^{4}}\right) e^{\frac{1}{x^{2}}}}{x^{5}}$$

Simplify

The graph

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Derivative of exp^x^-2

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The solution