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Graphing y =:
x^3/(x^2-x+1)
Identical expressions
x^ three /(x^ two -x+ one)
x cubed divide by (x squared minus x plus 1)
x to the power of three divide by (x to the power of two minus x plus one)
x3/(x2-x+1)
x3/x2-x+1
x³/(x²-x+1)
x to the power of 3/(x to the power of 2-x+1)
x^3/x^2-x+1
x^3 divide by (x^2-x+1)
Similar expressions
x^3/(x^2+x+1)
x^3/(x^2-x-1)
What you mean?
x^3/(x^2 - x + 1)
x^3/(x^2 - x) + 1
x^3/(x^2) - x + 1
x^3*2/x - x + 1
x^3/(x^2) - x + 1
x*3/(x^2 - x + 1)
x^3/(x^2) - x + 1

The derivative of the function/ x^3/(x^2-x+1)

You entered:

x^3/(x^2-x+1)

What you mean?

x^3/(x^2 - x + 1)

x^3/(x^2 - x) + 1

x^3/(x^2) - x + 1

x^3*2/x - x + 1

x^3/(x^2) - x + 1

x*3/(x^2 - x + 1)

x^3/(x^2) - x + 1

Derivative of x^3/(x^2-x+1)

The solution

You have entered [src]

     3    
    x     
----------
 2        
x  - x + 1

$$\frac{x^{3}}{x^{2} - x + 1}$$

  /     3    \
d |    x     |
--|----------|
dx| 2        |
  \x  - x + 1/

$$\frac{d}{d x} \frac{x^{3}}{x^{2} - x + 1}$$

Transform

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = x^{3}$ and $g{\left(x \right)} = x^{2} - x + 1$ .

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

$\frac{- x^{3} \cdot \left(2 x - 1\right) + 3 x^{2} \left(x^{2} - x + 1\right)}{\left(x^{2} - x + 1\right)^{2}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

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What you mean?

Derivative of x^3/(x^2-x+1)

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The solution