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The derivative of the function/ x^2/(x+6)

Derivative of x^2/(x+6)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   2 
  x  
-----
x + 6
$$\frac{x^{2}}{x + 6}$$ 
x^2/(x + 6)
Detail solution

  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Apply the power rule: goes to

    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 graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      2           
     x        2*x 
- -------- + -----
         2   x + 6
  (x + 6)
$$- \frac{x^{2}}{\left(x + 6\right)^{2}} + \frac{2 x}{x + 6}$$
Simplify
The second derivative [src] 
  /        2           \
  |       x        2*x |
2*|1 + -------- - -----|
  |           2   6 + x|
  \    (6 + x)         /
------------------------
         6 + x
$$\frac{2 \left(\frac{x^{2}}{\left(x + 6\right)^{2}} - \frac{2 x}{x + 6} + 1\right)}{x + 6}$$
Simplify
3-я производная [src] 
  /         2           \
  |        x        2*x |
6*|-1 - -------- + -----|
  |            2   6 + x|
  \     (6 + x)         /
-------------------------
                2        
         (6 + x)
$$\frac{6 \left(- \frac{x^{2}}{\left(x + 6\right)^{2}} + \frac{2 x}{x + 6} - 1\right)}{\left(x + 6\right)^{2}}$$
Simplify
The third derivative [src] 
  /         2           \
  |        x        2*x |
6*|-1 - -------- + -----|
  |            2   6 + x|
  \     (6 + x)         /
-------------------------
                2        
         (6 + x)
$$\frac{6 \left(- \frac{x^{2}}{\left(x + 6\right)^{2}} + \frac{2 x}{x + 6} - 1\right)}{\left(x + 6\right)^{2}}$$
Simplify
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