Mister Exam

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

Derivative of (x-2)²

The solution

You have entered [src]

       2
(x - 2)

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

(x - 2)^2

Detail solution

Let $u = x - 2$ .
Apply the power rule: $u^{2}$ goes to $2 u$
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 $-2$ is zero.
  The result is: $1$
The result of the chain rule is:

$2 x - 4$

The answer is:

$2 x - 4$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-4 + 2*x

$$2 x - 4$$

Simplify

The second derivative [src]

$$2$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of (x-2)²