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The derivative of the function/ (x-2)^4

Derivative of (x-2)^4

The solution

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       4
(x - 2)

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

(x - 2)^4

Detail solution

Let $u = x - 2$ .
Apply the power rule: $u^{4}$ goes to $4 u^{3}$
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 $-2$ is zero.
  The result is: $1$
The result of the chain rule is:

$4 \left(x - 2\right)^{3}$
Now simplify:

$4 \left(x - 2\right)^{3}$

The answer is:

$4 \left(x - 2\right)^{3}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

         3
4*(x - 2)

$$4 \left(x - 2\right)^{3}$$

Simplify

The second derivative [src]

           2
12*(-2 + x)

$$12 \left(x - 2\right)^{2}$$

Simplify

The third derivative [src]

24*(-2 + x)

$$24 \left(x - 2\right)$$

Simplify

The graph

Derivative of (x-2)^4