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Identical expressions
y=x^ two (x- six)
y equally x squared (x minus 6)
y equally x to the power of two (x minus six)
y=x2(x-6)
y=x2x-6
y=x²(x-6)
y=x to the power of 2(x-6)
y=x^2x-6
Similar expressions
y=x^2(x+6)

The derivative of the function/ y=x^2(x-6)

Derivative of y=x^2(x-6)

The solution

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 2        
x *(x - 6)

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

x^2*(x - 6)

Detail solution

Apply the product rule:

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

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

$3 x \left(x - 4\right)$

The answer is:

$3 x \left(x - 4\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

6*(-2 + x)

$$6 \left(x - 2\right)$$

Simplify

The third derivative [src]

$$6$$

Simplify

The graph

Derivative of y=x^2(x-6)