Mister Exam

Derivative of (3x-1)²

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

The graph:

from to

Piecewise:

The solution

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         2
(3*x - 1) 
(3x1)2\left(3 x - 1\right)^{2}
(3*x - 1)^2
Detail solution
  1. Let u=3x1u = 3 x - 1.

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

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

    1. Differentiate 3x13 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: 33

      2. The derivative of the constant 1-1 is zero.

      The result is: 33

    The result of the chain rule is:

    18x618 x - 6


The answer is:

18x618 x - 6

The graph
02468-8-6-4-2-1010-10001000
The first derivative [src]
-6 + 18*x
18x618 x - 6
The second derivative [src]
18
1818
The third derivative [src]
0
00
The graph
Derivative of (3x-1)²