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Graphing y =:
(4-2*x)/(1-x^2)
Limit of the function:
(4-2*x)/(1-x^2)
Identical expressions
(four - two *x)/(one -x^ two)
(4 minus 2 multiply by x) divide by (1 minus x squared )
(four minus two multiply by x) divide by (one minus x to the power of two)
(4-2*x)/(1-x2)
4-2*x/1-x2
(4-2*x)/(1-x²)
(4-2*x)/(1-x to the power of 2)
(4-2x)/(1-x^2)
(4-2x)/(1-x2)
4-2x/1-x2
4-2x/1-x^2
(4-2*x) divide by (1-x^2)
Similar expressions
(4+2*x)/(1-x^2)
(4-2*x)/(1+x^2)

The derivative of the function/ (4-2*x)/(1-x^2)

Derivative of (4-2*x)/(1-x^2)

The solution

You have entered [src]

4 - 2*x
-------
      2
 1 - x

$$\frac{4 - 2 x}{1 - x^{2}}$$

(4 - 2*x)/(1 - x^2)

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = 4 - 2 x$ and $g{\left(x \right)} = 1 - x^{2}$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $4 - 2 x$ term by term:
  1. The derivative of the constant $4$ 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: $x$ goes to $1$
    So, the result is: $-2$
  The result is: $-2$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $1 - x^{2}$ term by term:
  1. The derivative of the constant $1$ 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: $x^{2}$ goes to $2 x$
    So, the result is: $- 2 x$
  The result is: $- 2 x$
Now plug in to the quotient rule:

$\frac{2 x^{2} + 2 x \left(4 - 2 x\right) - 2}{\left(1 - x^{2}\right)^{2}}$
Now simplify:

$\frac{2 \left(x^{2} - 2 x \left(x - 2\right) - 1\right)}{\left(x^{2} - 1\right)^{2}}$

The answer is:

$\frac{2 \left(x^{2} - 2 x \left(x - 2\right) - 1\right)}{\left(x^{2} - 1\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    2      2*x*(4 - 2*x)
- ------ + -------------
       2             2  
  1 - x      /     2\   
             \1 - x /

$$\frac{2 x \left(4 - 2 x\right)}{\left(1 - x^{2}\right)^{2}} - \frac{2}{1 - x^{2}}$$

Simplify

The second derivative [src]

  /       /          2 \         \
  |       |       4*x  |         |
4*|-2*x + |-1 + -------|*(-2 + x)|
  |       |           2|         |
  \       \     -1 + x /         /
----------------------------------
                     2            
            /      2\             
            \-1 + x /

$$\frac{4 \left(- 2 x + \left(x - 2\right) \left(\frac{4 x^{2}}{x^{2} - 1} - 1\right)\right)}{\left(x^{2} - 1\right)^{2}}$$

Simplify

The third derivative [src]

   /                   /          2 \         \
   |                   |       2*x  |         |
   |               4*x*|-1 + -------|*(-2 + x)|
   |          2        |           2|         |
   |       4*x         \     -1 + x /         |
12*|-1 + ------- - ---------------------------|
   |           2                   2          |
   \     -1 + x              -1 + x           /
-----------------------------------------------
                            2                  
                   /      2\                   
                   \-1 + x /

$$\frac{12 \left(\frac{4 x^{2}}{x^{2} - 1} - \frac{4 x \left(x - 2\right) \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right)^{2}}$$

Simplify

The graph

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Derivative of (4-2*x)/(1-x^2)

The graph:

Piecewise:

The solution