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Derivative of Аe^(-x)*x^-1

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

The graph:

from to

Piecewise:

The solution

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

    and .

    To find :

    1. The derivative of the constant is zero.

    To find :

    1. Apply the product rule:

      ; to find :

      1. Apply the power rule: goes to

      ; to find :

      1. The derivative of is itself.

      The result is:

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

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