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Derivative of:
Derivative of (x-2)^3
Derivative of sqrt(x^2-1)
Derivative of ln(x)/x
Derivative of ln(x^2+1)
Integral of d{x}:
(x-2)^3
Graphing y =:
(x-2)^3
Canonical form:
(x-2)^3
Identical expressions
(x- two)^ three
(x minus 2) cubed
(x minus two) to the power of three
(x-2)3
x-23
(x-2)³
(x-2) to the power of 3
x-2^3
Similar expressions
y=(x-2)^3-x^2
(x+2)^3

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

Derivative of (x-2)^3

The solution

You have entered [src]

       3
(x - 2)

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

(x - 2)^3

Detail solution

Let $u = x - 2$ .
Apply the power rule: $u^{3}$ goes to $3 u^{2}$
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:

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

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

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)^3