Mister Exam

Derivative of e^x/x

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

The graph:

from to

Piecewise:

The solution

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

    and .

    To find :

    1. The derivative of is itself.

    To find :

    1. Apply the power rule: goes to

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
 x    x
e    e 
-- - --
x     2
     x 
$$\frac{e^{x}}{x} - \frac{e^{x}}{x^{2}}$$
The second derivative [src]
/    2   2 \  x
|1 - - + --|*e 
|    x    2|   
\        x /   
---------------
       x       
$$\frac{\left(1 - \frac{2}{x} + \frac{2}{x^{2}}\right) e^{x}}{x}$$
The third derivative [src]
/    6    3   6 \  x
|1 - -- - - + --|*e 
|     3   x    2|   
\    x        x /   
--------------------
         x          
$$\frac{\left(1 - \frac{3}{x} + \frac{6}{x^{2}} - \frac{6}{x^{3}}\right) e^{x}}{x}$$
The graph
Derivative of e^x/x