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Derivative of (x-2)^2(x-4)^2

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

The graph:

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Piecewise:

The solution

You have entered [src]
       2        2
(x - 2) *(x - 4) 
$$\left(x - 4\right)^{2} \left(x - 2\right)^{2}$$
(x - 2)^2*(x - 4)^2
Detail solution
  1. Apply the product rule:

    ; 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. Apply the power rule: goes to

        2. The derivative of the constant is zero.

        The result is:

      The result of the chain rule 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. Apply the power rule: goes to

        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                     2           
(x - 4) *(-4 + 2*x) + (x - 2) *(-8 + 2*x)
$$\left(x - 4\right)^{2} \left(2 x - 4\right) + \left(x - 2\right)^{2} \left(2 x - 8\right)$$
The second derivative [src]
  /        2           2                      \
2*\(-4 + x)  + (-2 + x)  + 4*(-4 + x)*(-2 + x)/
$$2 \left(\left(x - 4\right)^{2} + 4 \left(x - 4\right) \left(x - 2\right) + \left(x - 2\right)^{2}\right)$$
The third derivative [src]
24*(-3 + x)
$$24 \left(x - 3\right)$$
3-я производная [src]
24*(-3 + x)
$$24 \left(x - 3\right)$$