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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) 
$$x^{3} \left(x + 2\right)^{2}$$
d / 3        2\
--\x *(x + 2) /
dx             
$$\frac{d}{d x} x^{3} \left(x + 2\right)^{2}$$
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) 
$$x^{3} \cdot \left(2 x + 4\right) + 3 x^{2} \left(x + 2\right)^{2}$$
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)/
$$6 \cdot \left(3 x^{2} + 6 x \left(x + 2\right) + \left(x + 2\right)^{2}\right)$$
The graph
Derivative of x^3*(x+2)^2