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Derivative of:
Derivative of sin(x)^2
Derivative of cos(x/3)
Derivative of √x
Derivative of 5x-1
Identical expressions
exp(one /x^ three)
exponent of (1 divide by x cubed )
exponent of (one divide by x to the power of three)
exp(1/x3)
exp1/x3
exp(1/x³)
exp(1/x to the power of 3)
exp1/x^3
exp(1 divide by x^3)

The derivative of the function/ exp(1/x^3)

Derivative of exp(1/x^3)

The solution

You have entered [src]

 1 
 --
  3
 x 
e

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

exp(1/(x^3))

Detail solution

Let $u = \frac{1}{x^{3}}$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} \frac{1}{x^{3}}$ :
1. Let $u = x^{3}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{3}$ :
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  The result of the chain rule is:
  
  $- \frac{3}{x^{4}}$
The result of the chain rule is:

$- \frac{3 e^{\frac{1}{x^{3}}}}{x^{4}}$
Now simplify:

$- \frac{3 e^{\frac{1}{x^{3}}}}{x^{4}}$

The answer is:

$- \frac{3 e^{\frac{1}{x^{3}}}}{x^{4}}$

The first derivative [src]

    1 
    --
     3
    x 
-3*e  
------
   4  
  x

$$- \frac{3 e^{\frac{1}{x^{3}}}}{x^{4}}$$

Simplify

The second derivative [src]

            1 
            --
             3
  /    3 \  x 
3*|4 + --|*e  
  |     3|    
  \    x /    
--------------
       5      
      x

$$\frac{3 \left(4 + \frac{3}{x^{3}}\right) e^{\frac{1}{x^{3}}}}{x^{5}}$$

Simplify

The third derivative [src]

                   1 
                   --
                    3
   /     9    36\  x 
-3*|20 + -- + --|*e  
   |      6    3|    
   \     x    x /    
---------------------
           6         
          x

$$- \frac{3 \left(20 + \frac{36}{x^{3}} + \frac{9}{x^{6}}\right) e^{\frac{1}{x^{3}}}}{x^{6}}$$

Simplify

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Identical expressions

Derivative of exp(1/x^3)

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The solution