Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of 2/e^x
Derivative of x^3*lnx
Derivative of 2/(x+1)
Derivative of sin(3)^(2)*x
Identical expressions
(x- one)(x^ two +x+ one)
(x minus 1)(x squared plus x plus 1)
(x minus one)(x to the power of two plus x plus one)
(x-1)(x2+x+1)
x-1x2+x+1
(x-1)(x²+x+1)
(x-1)(x to the power of 2+x+1)
x-1x^2+x+1
Similar expressions
(x+1)(x^2+x+1)
(x-1)(x^2-x+1)
(x-1)(x^2+x-1)

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

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

The solution

You have entered [src]

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

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

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

Detail solution

Apply the product rule:

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

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

$3 x^{2}$

The answer is:

$3 x^{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

6*x

$$6 x$$

Simplify

The third derivative [src]

$$6$$

Simplify

The graph

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