Question

if $f(x)=(x - 2)(6x - 4)$, find $f(x)$. $f(x)=$

Explanation:

Step1: Apply product - rule

The product - rule states that if $y = u\cdot v$, then $y'=u'v + uv'$. Let $u=x - 2$ and $v = 6x-4$. First, find $u'$ and $v'$.
$u'=\frac{d}{dx}(x - 2)=1$ and $v'=\frac{d}{dx}(6x - 4)=6$.

Step2: Calculate $f'(x)$

Using the product - rule $f'(x)=u'v+uv'$, substitute $u$, $v$, $u'$, and $v'$ into the formula.
$f'(x)=1\cdot(6x - 4)+(x - 2)\cdot6$.

Step3: Simplify the expression

Expand and combine like - terms:
\[

$$\begin{align*} f'(x)&=6x-4 + 6x-12\\ &=(6x+6x)+(-4 - 12)\\ &=12x-16 \end{align*}$$

\]

Answer:

$12x - 16$