Calculus and Its Applications, Chapter 1, 1.6, Section 1.6, Problem 4

Take the derivative of $g(x) = (3x - 2)(4x + 1)$: first, use the Product Rule; then,
by multiplying the expression before differentiating. Compare your results as a check.

By using Product Rule,

$
\begin{equation}
\begin{aligned}
g'(x) = \frac{d}{dx} \left[ (3x - 2)(4x + 1) \right] &= (3x - 2) \cdot \frac{d}{dx} (4x + 1) + (4x + 1) \cdot \frac{d}{dx} (3x - 2)\\
\\
&= (3x - 2)(4) + (4x + 1)(3)\\
\\
&= 12x - 8 + 12x + 3\\
\\
&= 24x - 5
\end{aligned}
\end{equation}
$


By multiplying the expression first,

$
\begin{equation}
\begin{aligned}
g(x) &= (3x - 2)(4x + 1) = 12x^2 + 3x - 8x - 2 = 12x^2 - 5x - 2\\
\\
g'(x) &= \frac{d}{dx} \left[ 12x^2 - 5x - 2 \right] = 24x - 5
\end{aligned}
\end{equation}
$


Both results agree.