Mister Exam

Derivative of (2x-1)^2

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

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         2
(2*x - 1) 
(2x1)2\left(2 x - 1\right)^{2}
d /         2\
--\(2*x - 1) /
dx            
ddx(2x1)2\frac{d}{d x} \left(2 x - 1\right)^{2}
Detail solution
  1. Let u=2x1u = 2 x - 1.

  2. Apply the power rule: u2u^{2} goes to 2u2 u

  3. Then, apply the chain rule. Multiply by ddx(2x1)\frac{d}{d x} \left(2 x - 1\right):

    1. Differentiate 2x12 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: xx goes to 11

        So, the result is: 22

      2. The derivative of the constant (1)1\left(-1\right) 1 is zero.

      The result is: 22

    The result of the chain rule is:

    8x48 x - 4


The answer is:

8x48 x - 4

The graph
02468-8-6-4-2-1010-500500
The first derivative [src]
-4 + 8*x
8x48 x - 4
The second derivative [src]
8
88
The third derivative [src]
0
00
The graph
Derivative of (2x-1)^2