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Derivative of (1-x^2)/x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
     2
1 - x 
------
  x   
$$\frac{1 - x^{2}}{x}$$
(1 - x^2)/x
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result is:

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