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The derivative of the function/ (x^2-9)/(x+3)

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

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

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The solution

You have entered [src] 
 2    
x  - 9
------
x + 3
x2−9x+3\frac{x^{2} - 9}{x + 3} 
  / 2    \
d |x  - 9|
--|------|
dx\x + 3 /
ddxx2−9x+3\frac{d}{d x} \frac{x^{2} - 9}{x + 3}
Transform
Detail solution

  1. Apply the quotient rule, which is:

    ddxf(x)g(x)=−f(x)ddxg(x)+g(x)ddxf(x)g2(x)\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(x)=x2−9f{\left(x \right)} = x^{2} - 9 and g(x)=x+3g{\left(x \right)} = x + 3.

    To find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Differentiate x2−9x^{2} - 9 term by term:

      1. The derivative of the constant −9-9 is zero.

      2. Apply the power rule: x2x^{2} goes to 2x2 x

      The result is: 2x2 x

    To find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. Differentiate x+3x + 3 term by term:

      1. The derivative of the constant 33 is zero.

      2. Apply the power rule: xx goes to 11

      The result is: 11

    Now plug in to the quotient rule:

    −x2+2x(x+3)+9(x+3)2\frac{- x^{2} + 2 x \left(x + 3\right) + 9}{\left(x + 3\right)^{2}}

  2. Now simplify:

    11

The answer is:

11

The first derivative [src] 
    2             
   x  - 9     2*x 
- -------- + -----
         2   x + 3
  (x + 3)
2xx+3−x2−9(x+3)2\frac{2 x}{x + 3} - \frac{x^{2} - 9}{\left(x + 3\right)^{2}}
Simplify
The second derivative [src] 
  /          2         \
  |    -9 + x      2*x |
2*|1 + -------- - -----|
  |           2   3 + x|
  \    (3 + x)         /
------------------------
         3 + x
2(−2xx+3+1+x2−9(x+3)2)x+3\frac{2 \left(- \frac{2 x}{x + 3} + 1 + \frac{x^{2} - 9}{\left(x + 3\right)^{2}}\right)}{x + 3}
Simplify
The third derivative [src] 
  /           2         \
  |     -9 + x      2*x |
6*|-1 - -------- + -----|
  |            2   3 + x|
  \     (3 + x)         /
-------------------------
                2        
         (3 + x)
6⋅(2xx+3−1−x2−9(x+3)2)(x+3)2\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}}
Simplify
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