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

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Derivative of:
Derivative of sin(4x)
Derivative of x^e
Derivative of (x^3-1)(x^2+x+1)
Derivative of ln1
Identical expressions
(x^ three - one)(x^ two +x+ one)
(x cubed minus 1)(x squared plus x plus 1)
(x to the power of three minus one)(x to the power of two plus x plus one)
(x3-1)(x2+x+1)
x3-1x2+x+1
(x³-1)(x²+x+1)
(x to the power of 3-1)(x to the power of 2+x+1)
x^3-1x^2+x+1
Similar expressions
(x^3+1)(x^2+x+1)
(x^3-1)(x^2+x-1)
(x^3-1)(x^2-x+1)

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

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

The solution

You have entered [src]

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

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

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

Detail solution

Apply the product rule:

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

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

$5 x^{4} + 4 x^{3} + 3 x^{2} - 2 x - 1$

The answer is:

$5 x^{4} + 4 x^{3} + 3 x^{2} - 2 x - 1$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

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