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

How to use it?
Derivative of:
Derivative of x^(-2)
Derivative of (x^2-1)^3
Derivative of sqrt(1/x)
Derivative of sin(x)^(9)
Graphing y =:
((x-2)^2)*(x+2)
Identical expressions
y=((x- two)^ two)*(x+ two)
y equally ((x minus 2) squared ) multiply by (x plus 2)
y equally ((x minus two) to the power of two) multiply by (x plus two)
y=((x-2)2)*(x+2)
y=x-22*x+2
y=((x-2)²)*(x+2)
y=((x-2) to the power of 2)*(x+2)
y=((x-2)^2)(x+2)
y=((x-2)2)(x+2)
y=x-22x+2
y=x-2^2x+2
Similar expressions
y=((x+2)^2)*(x+2)
y=((x-2)^2)*(x-2)

The derivative of the function/ y=((x-2)^2)*(x+2)

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

The solution

You have entered [src]

       2        
(x - 2) *(x + 2)

$$\left(x + 2\right) \left(x - 2\right)^{2}$$

d /       2        \
--\(x - 2) *(x + 2)/
dx

$$\frac{d}{d x} \left(x + 2\right) \left(x - 2\right)^{2}$$

Transform

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = \left(x - 2\right)^{2}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Let $u = x - 2$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x - 2\right)$ :
  1. Differentiate $x - 2$ term by term:
    1. Apply the power rule: $x$ goes to $1$
    2. The derivative of the constant $\left(-1\right) 2$ is zero.
    The result is: $1$
  The result of the chain rule is:
  
  $2 x - 4$
$g{\left(x \right)} = x + 2$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x + 2$ term by term:
  1. Apply the power rule: $x$ goes to $1$
  2. The derivative of the constant $2$ is zero.
  The result is: $1$
The result is: $\left(x + 2\right) \left(2 x - 4\right) + \left(x - 2\right)^{2}$
Now simplify:

$\left(x - 2\right) \left(3 x + 2\right)$

The answer is:

$\left(x - 2\right) \left(3 x + 2\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       2                     
(x - 2)  + (-4 + 2*x)*(x + 2)

$$\left(x + 2\right) \left(2 x - 4\right) + \left(x - 2\right)^{2}$$

Simplify

The second derivative [src]

2*(-2 + 3*x)

$$2 \cdot \left(3 x - 2\right)$$

Simplify

The third derivative [src]

$$6$$

Simplify

The graph

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