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Derivative of (x^2-8*x)/(x+1)
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Graphing y =:
(x^2-8*x)/(x+1)
Identical expressions
(x^ two - eight *x)/(x+ one)
(x squared minus 8 multiply by x) divide by (x plus 1)
(x to the power of two minus eight multiply by x) divide by (x plus one)
(x2-8*x)/(x+1)
x2-8*x/x+1
(x²-8*x)/(x+1)
(x to the power of 2-8*x)/(x+1)
(x^2-8x)/(x+1)
(x2-8x)/(x+1)
x2-8x/x+1
x^2-8x/x+1
(x^2-8*x) divide by (x+1)
Similar expressions
(x^2+8*x)/(x+1)
(x^2-8*x)/(x-1)

The derivative of the function/ (x^2-8*x)/(x+1)

Derivative of (x^2-8*x)/(x+1)

The solution

You have entered [src]

 2      
x  - 8*x
--------
 x + 1

$$\frac{x^{2} - 8 x}{x + 1}$$

(x^2 - 8*x)/(x + 1)

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = x^{2} - 8 x$ and $g{\left(x \right)} = x + 1$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x^{2} - 8 x$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $-8$
  The result is: $2 x - 8$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x + 1$ term by term:
  1. The derivative of the constant $1$ is zero.
  2. Apply the power rule: $x$ goes to $1$
  The result is: $1$
Now plug in to the quotient rule:

$\frac{- x^{2} + 8 x + \left(x + 1\right) \left(2 x - 8\right)}{\left(x + 1\right)^{2}}$
Now simplify:

$\frac{x^{2} + 2 x - 8}{x^{2} + 2 x + 1}$

The answer is:

$\frac{x^{2} + 2 x - 8}{x^{2} + 2 x + 1}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

            2      
-8 + 2*x   x  - 8*x
-------- - --------
 x + 1            2
           (x + 1)

$$\frac{2 x - 8}{x + 1} - \frac{x^{2} - 8 x}{\left(x + 1\right)^{2}}$$

Simplify

The second derivative [src]

  /    2*(-4 + x)   x*(-8 + x)\
2*|1 - ---------- + ----------|
  |      1 + x              2 |
  \                  (1 + x)  /
-------------------------------
             1 + x

$$\frac{2 \left(\frac{x \left(x - 8\right)}{\left(x + 1\right)^{2}} - \frac{2 \left(x - 4\right)}{x + 1} + 1\right)}{x + 1}$$

Simplify

The third derivative [src]

  /     2*(-4 + x)   x*(-8 + x)\
6*|-1 + ---------- - ----------|
  |       1 + x              2 |
  \                   (1 + x)  /
--------------------------------
                   2            
            (1 + x)

$$\frac{6 \left(- \frac{x \left(x - 8\right)}{\left(x + 1\right)^{2}} + \frac{2 \left(x - 4\right)}{x + 1} - 1\right)}{\left(x + 1\right)^{2}}$$

Simplify

The graph

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Derivative of (x^2-8*x)/(x+1)

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The solution