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Derivative of:
Derivative of (-2)/x^3
Derivative of ln(x^2-4x)
Derivative of e^(3/x)
Derivative of (2*x+1)*(x^2+3*x-1)
Limit of the function:
e^(3/x)
Integral of d{x}:
e^(3/x)
Identical expressions
e^(three /x)
e to the power of (3 divide by x)
e to the power of (three divide by x)
e(3/x)
e3/x
e^3/x
e^(3 divide by x)

The derivative of the function/ e^(3/x)

Derivative of e^(3/x)

The solution

You have entered [src]

 3
 -
 x
E

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

E^(3/x)

Detail solution

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

                 3
                 -
   /    3    6\  x
-9*|2 + -- + -|*e 
   |     2   x|   
   \    x     /   
------------------
         4        
        x

$$- \frac{9 \left(2 + \frac{6}{x} + \frac{3}{x^{2}}\right) e^{\frac{3}{x}}}{x^{4}}$$

Simplify

The graph

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Identical expressions

Derivative of e^(3/x)

The graph:

Piecewise:

The solution