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

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

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

The solution

You have entered [src]

 2    
x  - 3
------
x - 2

$$\frac{x^{2} - 3}{x - 2}$$

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

Detail solution

Apply the quotient rule, which is:

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

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

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

  /            2          \
  |      -3 + x      2*x  |
6*|-1 - --------- + ------|
  |             2   -2 + x|
  \     (-2 + x)          /
---------------------------
                 2         
         (-2 + x)

$$\frac{6 \left(\frac{2 x}{x - 2} - 1 - \frac{x^{2} - 3}{\left(x - 2\right)^{2}}\right)}{\left(x - 2\right)^{2}}$$

Simplify

The graph

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Identical expressions

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

The graph:

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The solution