Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of 3^(2*x)
Derivative of (x-3)^4
Derivative of ln(1+x)
Derivative of ln(1-x)
Integral of d{x}:
(x-3)^4
Canonical form:
(x-3)^4
Identical expressions
(x- three)^ four
(x minus 3) to the power of 4
(x minus three) to the power of four
(x-3)4
x-34
(x-3)⁴
x-3^4
Similar expressions
(x+3)^4

The derivative of the function/ (x-3)^4

Derivative of (x-3)^4

The solution

You have entered [src]

       4
(x - 3)

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

d /       4\
--\(x - 3) /
dx

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

Transform

Detail solution

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

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

         3
4*(x - 3)

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

Simplify

The second derivative [src]

           2
12*(-3 + x)

$$12 \left(x - 3\right)^{2}$$

Simplify

The third derivative [src]

24*(-3 + x)

$$24 \left(x - 3\right)$$

Simplify

The graph

Derivative of (x-3)^4