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.