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x^3*(x-2)^2

Derivative of x^3*(x-2)^2

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

The graph:

from to

Piecewise:

The solution

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

    ; to find :

    1. Apply the power rule: goes to

    ; 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]
 3                 2        2
x *(-4 + 2*x) + 3*x *(x - 2) 
$$x^{3} \left(2 x - 4\right) + 3 x^{2} \left(x - 2\right)^{2}$$
The second derivative [src]
    / 2             2               \
2*x*\x  + 3*(-2 + x)  + 6*x*(-2 + x)/
$$2 x \left(x^{2} + 6 x \left(x - 2\right) + 3 \left(x - 2\right)^{2}\right)$$
The third derivative [src]
  /        2      2               \
6*\(-2 + x)  + 3*x  + 6*x*(-2 + x)/
$$6 \left(3 x^{2} + 6 x \left(x - 2\right) + \left(x - 2\right)^{2}\right)$$
The graph
Derivative of x^3*(x-2)^2