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Derivative of x*e^((-1)/x^3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   -1 
   ---
     3
    x 
x*E   
$$e^{- \frac{1}{x^{3}}} x$$
x*E^(-1/x^3)
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Apply the power rule: goes to

    To find :

    1. Let .

    2. The derivative of is itself.

    3. Then, apply the chain rule. Multiply by :

      1. Let .

      2. Apply the power rule: goes to

      3. Then, apply the chain rule. Multiply by :

        1. Apply the power rule: goes to

        The result of the chain rule is:

      The result of the chain rule is:

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The first derivative [src]
          -1 
 -1       ---
 ---        3
   3       x 
  x    3*e   
E    + ------
          3  
         x   
$$e^{- \frac{1}{x^{3}}} + \frac{3 e^{- \frac{1}{x^{3}}}}{x^{3}}$$
The second derivative [src]
             -1 
             ---
               3
  /     3 \   x 
3*|-2 + --|*e   
  |      3|     
  \     x /     
----------------
        4       
       x        
$$\frac{3 \left(-2 + \frac{3}{x^{3}}\right) e^{- \frac{1}{x^{3}}}}{x^{4}}$$
The third derivative [src]
                 -1 
                 ---
                   3
  /    27   9 \   x 
3*|8 - -- + --|*e   
  |     3    6|     
  \    x    x /     
--------------------
          5         
         x          
$$\frac{3 \left(8 - \frac{27}{x^{3}} + \frac{9}{x^{6}}\right) e^{- \frac{1}{x^{3}}}}{x^{5}}$$