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Graphing y =:
(x^2-2*x+3)/x^2
Identical expressions
(x^ two - two *x+ three)/x^ two
(x squared minus 2 multiply by x plus 3) divide by x squared
(x to the power of two minus two multiply by x plus three) divide by x to the power of two
(x2-2*x+3)/x2
x2-2*x+3/x2
(x²-2*x+3)/x²
(x to the power of 2-2*x+3)/x to the power of 2
(x^2-2x+3)/x^2
(x2-2x+3)/x2
x2-2x+3/x2
x^2-2x+3/x^2
(x^2-2*x+3) divide by x^2
Similar expressions
(x^2+2*x+3)/x^2
(x^2-2*x-3)/x^2

The derivative of the function/ (x^2-2*x+3)/x^2

Derivative of (x^2-2*x+3)/x^2

The solution

You have entered [src]

 2          
x  - 2*x + 3
------------
      2     
     x

$$\frac{\left(x^{2} - 2 x\right) + 3}{x^{2}}$$

(x^2 - 2*x + 3)/x^2

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = x^{2} - 2 x + 3$ and $g{\left(x \right)} = x^{2}$ .

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

$\frac{x^{2} \left(2 x - 2\right) - 2 x \left(x^{2} - 2 x + 3\right)}{x^{4}}$
Now simplify:

$\frac{2 \left(x - 3\right)}{x^{3}}$

The answer is:

$\frac{2 \left(x - 3\right)}{x^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

             / 2          \
-2 + 2*x   2*\x  - 2*x + 3/
-------- - ----------------
    2              3       
   x              x

$$\frac{2 x - 2}{x^{2}} - \frac{2 \left(\left(x^{2} - 2 x\right) + 3\right)}{x^{3}}$$

Simplify

The second derivative [src]

  /                   /     2      \\
  |    4*(-1 + x)   3*\3 + x  - 2*x/|
2*|1 - ---------- + ----------------|
  |        x                2       |
  \                        x        /
-------------------------------------
                   2                 
                  x

$$\frac{2 \left(1 - \frac{4 \left(x - 1\right)}{x} + \frac{3 \left(x^{2} - 2 x + 3\right)}{x^{2}}\right)}{x^{2}}$$

Simplify

The third derivative [src]

   /       /     2      \             \
   |     2*\3 + x  - 2*x/   3*(-1 + x)|
12*|-1 - ---------------- + ----------|
   |             2              x     |
   \            x                     /
---------------------------------------
                    3                  
                   x

$$\frac{12 \left(-1 + \frac{3 \left(x - 1\right)}{x} - \frac{2 \left(x^{2} - 2 x + 3\right)}{x^{2}}\right)}{x^{3}}$$

Simplify

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Derivative of (x^2-2*x+3)/x^2

The graph:

Piecewise:

The solution