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

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

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

The solution

You have entered [src]

 2          
x  - 2*x + 1
------------
   x + 2

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

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

Detail solution

Apply the quotient rule, which is:

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

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

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x^{2} - 2 x + 1$ term by term:
  1. The derivative of the constant $1$ is zero.
  2. Apply the power rule: $x^{2}$ goes to $2 x$
  3. 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: $2 x - 2$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x + 2$ term by term:
  1. The derivative of the constant $2$ is zero.
  2. Apply the power rule: $x$ goes to $1$
  The result is: $1$
Now plug in to the quotient rule:

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

$\frac{x^{2} + 4 x - 5}{x^{2} + 4 x + 4}$

The answer is:

$\frac{x^{2} + 4 x - 5}{x^{2} + 4 x + 4}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

            2          
-2 + 2*x   x  - 2*x + 1
-------- - ------------
 x + 2              2  
             (x + 2)

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

  /          2                   \
  |     1 + x  - 2*x   2*(-1 + x)|
6*|-1 - ------------ + ----------|
  |              2       2 + x   |
  \       (2 + x)                /
----------------------------------
                    2             
             (2 + x)

$$\frac{6 \left(\frac{2 \left(x - 1\right)}{x + 2} - 1 - \frac{x^{2} - 2 x + 1}{\left(x + 2\right)^{2}}\right)}{\left(x + 2\right)^{2}}$$

Simplify

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

The graph:

Piecewise:

The solution