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Derivative of:
Derivative of (x^2-9)/(x+3)
Derivative of y=tg8x
Derivative of sqrt(6-2x)
Derivative of sqrt(1-x^2)
Integral of d{x}:
(x^2-9)/(x+3)
How do you in partial fractions?:
(x^2-9)/(x+3)
Graphing y =:
(x^2-9)/(x+3)
Identical expressions
(x^ two - nine)/(x+ three)
(x squared minus 9) divide by (x plus 3)
(x to the power of two minus nine) divide by (x plus three)
(x2-9)/(x+3)
x2-9/x+3
(x²-9)/(x+3)
(x to the power of 2-9)/(x+3)
x^2-9/x+3
(x^2-9) divide by (x+3)
Similar expressions
(x^2+9)/(x+3)
(x^2-9)/(x-3)

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

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

The solution

You have entered [src]

 2    
x  - 9
------
x + 3

$$\frac{x^{2} - 9}{x + 3}$$

  / 2    \
d |x  - 9|
--|------|
dx\x + 3 /

$$\frac{d}{d x} \frac{x^{2} - 9}{x + 3}$$

Transform

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = x^{2} - 9$ and $g{\left(x \right)} = x + 3$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x^{2} - 9$ term by term:
  1. The derivative of the constant $-9$ 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 $x + 3$ term by term:
  1. The derivative of the constant $3$ is zero.
  2. Apply the power rule: $x$ goes to $1$
  The result is: $1$
Now plug in to the quotient rule:

$\frac{- x^{2} + 2 x \left(x + 3\right) + 9}{\left(x + 3\right)^{2}}$
Now simplify:

$1$

The answer is:

$1$

The first derivative [src]

    2             
   x  - 9     2*x 
- -------- + -----
         2   x + 3
  (x + 3)

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

Simplify

The second derivative [src]

  /          2         \
  |    -9 + x      2*x |
2*|1 + -------- - -----|
  |           2   3 + x|
  \    (3 + x)         /
------------------------
         3 + x

$$\frac{2 \left(- \frac{2 x}{x + 3} + 1 + \frac{x^{2} - 9}{\left(x + 3\right)^{2}}\right)}{x + 3}$$

Simplify

The third derivative [src]

  /           2         \
  |     -9 + x      2*x |
6*|-1 - -------- + -----|
  |            2   3 + x|
  \     (3 + x)         /
-------------------------
                2        
         (3 + x)

$$\frac{6 \cdot \left(\frac{2 x}{x + 3} - 1 - \frac{x^{2} - 9}{\left(x + 3\right)^{2}}\right)}{\left(x + 3\right)^{2}}$$

Simplify

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

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