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Derivative of (x^2-9)/(x+3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 2    
x  - 9
------
x + 3 
$$\frac{x^{2} - 9}{x + 3}$$
  / 2    \
d |x  - 9|
--|------|
dx\x + 3 /
$$\frac{d}{d x} \frac{x^{2} - 9}{x + 3}$$
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. Apply the power rule: goes to

      The result is:

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

      The result is:

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The first derivative [src]
    2             
   x  - 9     2*x 
- -------- + -----
         2   x + 3
  (x + 3)         
$$\frac{2 x}{x + 3} - \frac{x^{2} - 9}{\left(x + 3\right)^{2}}$$
The second derivative [src]
  /          2         \
  |    -9 + x      2*x |
2*|1 + -------- - -----|
  |           2   3 + x|
  \    (3 + x)         /
------------------------
         3 + x          
$$\frac{2 \left(- \frac{2 x}{x + 3} + 1 + \frac{x^{2} - 9}{\left(x + 3\right)^{2}}\right)}{x + 3}$$
The third derivative [src]
  /           2         \
  |     -9 + x      2*x |
6*|-1 - -------- + -----|
  |            2   3 + x|
  \     (3 + x)         /
-------------------------
                2        
         (3 + x)         
$$\frac{6 \cdot \left(\frac{2 x}{x + 3} - 1 - \frac{x^{2} - 9}{\left(x + 3\right)^{2}}\right)}{\left(x + 3\right)^{2}}$$