calculate the derivative of $f(x)=(x - 1)(x - 7)(x - 6)$ using the appropriate rule or combination of rules.
$f(x)=$

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Accepted Answer

# Explanation:
## Step1: Expand the function
$$
\begin{align*}
f(x)&=(x - 1)(x - 7)(x - 6)\
&=(x^2-7x - x + 7)(x - 6)\
&=(x^2-8x + 7)(x - 6)\
&=x^3-6x^2-8x^2 + 48x+7x - 42\
&=x^3-14x^2 + 55x - 42
\end{align*}
$$
## Step2: Differentiate term - by - term
The derivative of $x^n$ is $nx^{n - 1}$.
The derivative of $x^3$ is $3x^{2}$, the derivative of $-14x^2$ is $-28x$, the derivative of $55x$ is $55$, and the derivative of the constant $-42$ is $0$.
So $f'(x)=3x^{2}-28x + 55$.

# Answer:
$3x^{2}-28x + 55$

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Explanation:

Step1: Expand the function

Step2: Differentiate term - by - term

Answer: