Calculus and Its Applications, Chapter 1, 1.6, Section 1.6, Problem 6

Take the derivative of $F(x) = 3x^4(x^2 - 4x)$: 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}
F'(x) = \frac{d}{dx} \left[ 3x^4 (x^2 - 4x) \right] &= 3x^4 \cdot \frac{d}{dx} (x^2 - 4x) + (x^2 - 4x) \cdot \frac{d}{dx} (3x^4)\\
\\
&= 3x^4 (2x - 4) + (x^2 - 4x)(12x^3)\\
\\
&= 6x^5 - 12x^4 + 12x^5 - 48x^4\\
\\
&= 18x^5 - 60x^4
\end{aligned}
\end{equation}
$


By multiplying the expression first,

$
\begin{equation}
\begin{aligned}
F(x) &= 3x^4 (x^2 - 4x) = 3x^6 - 12x^5 \\
\\
F'(x) &= \frac{d}{dx} \left[ 3x^6 - 12x^5 \right] = 18x^5 - 60x^4
\end{aligned}
\end{equation}
$


Both results agree.