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Identical expressions
(x- two)^ two *(x- two)
(x minus 2) squared multiply by (x minus 2)
(x minus two) to the power of two multiply by (x minus two)
(x-2)2*(x-2)
x-22*x-2
(x-2)²*(x-2)
(x-2) to the power of 2*(x-2)
(x-2)^2(x-2)
(x-2)2(x-2)
x-22x-2
x-2^2x-2
Similar expressions
(x-2)^2*(x+2)
(x+2)^2*(x-2)

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

Derivative of (x-2)^2*(x-2)

The solution

You have entered [src]

       2        
(x - 2) *(x - 2)

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

d /       2        \
--\(x - 2) *(x - 2)/
dx

$$\frac{d}{d x} \left(x - 2\right) \left(x - 2\right)^{2}$$

Transform

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = \left(x - 2\right)^{2}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Let $u = x - 2$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x - 2\right)$ :
  1. Differentiate $x - 2$ term by term:
    1. Apply the power rule: $x$ goes to $1$
    2. The derivative of the constant $\left(-1\right) 2$ is zero.
    The result is: $1$
  The result of the chain rule is:
  
  $2 x - 4$
$g{\left(x \right)} = x - 2$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x - 2$ term by term:
  1. Apply the power rule: $x$ goes to $1$
  2. The derivative of the constant $\left(-1\right) 2$ is zero.
  The result is: $1$
The result is: $\left(x - 2\right)^{2} + \left(x - 2\right) \left(2 x - 4\right)$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       2                     
(x - 2)  + (-4 + 2*x)*(x - 2)

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

Simplify

The second derivative [src]

6*(-2 + x)

$$6 \left(x - 2\right)$$

Simplify

The third derivative [src]

$$6$$

Simplify

The graph

Derivative of (x-2)^2*(x-2)