Mister Exam

Derivative of 3x×(2x-1)²

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
             2
3*x*(2*x - 1) 
$$3 x \left(2 x - 1\right)^{2}$$
(3*x)*(2*x - 1)^2
Detail solution
  1. Apply the product rule:

    ; to find :

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: goes to

      So, the result is:

    ; to find :

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. Differentiate 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: goes to

          So, the result is:

        2. The derivative of the constant is zero.

        The result is:

      The result of the chain rule is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
           2                 
3*(2*x - 1)  + 3*x*(-4 + 8*x)
$$3 x \left(8 x - 4\right) + 3 \left(2 x - 1\right)^{2}$$
The second derivative [src]
24*(-1 + 3*x)
$$24 \left(3 x - 1\right)$$
The third derivative [src]
72
$$72$$