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Derivative of:
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Identical expressions
y=(x- three)(x+ three)^ two
y equally (x minus 3)(x plus 3) squared
y equally (x minus three)(x plus three) to the power of two
y=(x-3)(x+3)2
y=x-3x+32
y=(x-3)(x+3)²
y=(x-3)(x+3) to the power of 2
y=x-3x+3^2
Similar expressions
y=(x-3)(x-3)^2
y=(x+3)(x+3)^2

The derivative of the function/ y=(x-3)(x+3)^2

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

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

Apply the product rule:

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

$f{\left(x \right)} = x - 3$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x - 3$ term by term:
  1. Apply the power rule: $x$ goes to $1$
  2. The derivative of the constant $-3$ is zero.
  The result is: $1$
$g{\left(x \right)} = \left(x + 3\right)^{2}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Let $u = x + 3$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + 3\right)$ :
  1. Differentiate $x + 3$ term by term:
    1. Apply the power rule: $x$ goes to $1$
    2. The derivative of the constant $3$ is zero.
    The result is: $1$
  The result of the chain rule is:
  
  $2 x + 6$
The result is: $\left(x - 3\right) \left(2 x + 6\right) + \left(x + 3\right)^{2}$
Now simplify:

$3 \left(x - 1\right) \left(x + 3\right)$

The answer is:

$3 \left(x - 1\right) \left(x + 3\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       2                    
(x + 3)  + (6 + 2*x)*(x - 3)

$$\left(x - 3\right) \left(2 x + 6\right) + \left(x + 3\right)^{2}$$

Simplify

The second derivative [src]

6*(1 + x)

$$6 \left(x + 1\right)$$

Simplify

The third derivative [src]

$$6$$

Simplify

The graph

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