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Derivative of:
Derivative of e^(2-x)
Derivative of (3-2*x)*cos(x)+2*sin(x)+4
Derivative of e^sin(x)^(2)
Derivative of (cos(x))^sin(x)
Identical expressions
(two *x- one)^ four
(2 multiply by x minus 1) to the power of 4
(two multiply by x minus one) to the power of four
(2*x-1)4
2*x-14
(2*x-1)⁴
(2x-1)^4
(2x-1)4
2x-14
2x-1^4
Similar expressions
(2*x+1)^4

The derivative of the function/ (2*x-1)^4

Derivative of (2*x-1)^4

The solution

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         4
(2*x - 1)

$$\left(2 x - 1\right)^{4}$$

d /         4\
--\(2*x - 1) /
dx

$$\frac{d}{d x} \left(2 x - 1\right)^{4}$$

Transform

Detail solution

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

$8 \left(2 x - 1\right)^{3}$
Now simplify:

$8 \left(2 x - 1\right)^{3}$

The answer is:

$8 \left(2 x - 1\right)^{3}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

           3
8*(2*x - 1)

$$8 \left(2 x - 1\right)^{3}$$

Simplify

The second derivative [src]

             2
48*(-1 + 2*x)

$$48 \left(2 x - 1\right)^{2}$$

Simplify

The third derivative [src]

192*(-1 + 2*x)

$$192 \cdot \left(2 x - 1\right)$$

Simplify

The graph

Derivative of (2*x-1)^4