Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of 6^x
Derivative of (x-2)^4
Derivative of sqrt(1-x)
Derivative of sin(3*x+2)
Graphing y =:
(x-2)^4
Integral of d{x}:
(x-2)^4
Identical expressions
(x- two)^ four
(x minus 2) to the power of 4
(x minus two) to the power of four
(x-2)4
x-24
(x-2)⁴
x-2^4
Similar expressions
(x+2)^4

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

Derivative of (x-2)^4

The solution

You have entered [src]

       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