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y=(x-3)(x+3)^2

Derivative of y=(x-3)(x+3)^2

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

The graph:

from to

Piecewise:

The solution

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

    ; to find :

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      2. The derivative of the constant is zero.

      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. 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                    
(x + 3)  + (6 + 2*x)*(x - 3)
$$\left(x - 3\right) \left(2 x + 6\right) + \left(x + 3\right)^{2}$$
The second derivative [src]
6*(1 + x)
$$6 \left(x + 1\right)$$
The third derivative [src]
6
$$6$$
The graph
Derivative of y=(x-3)(x+3)^2