#[Example][Ejemplo]#
$\displaystyle \frac{d}{dx}[ (3x^3 + 7x^2)(4x^2 - x + 4) ]$ \t $\displaystyle {}=$ #[Deriv of first][Deriv del primero]# × #[Second][Segundo]# + #[First][Primero]# × #[Deriv of second][Deriv del segundo]#
\\ \t $\displaystyle {}=\color{blue}{(9x^2 + 14x)}(4x^2 - x + 4) + (3x^3 + 7x^2)\color{blue}{(8x - 1)}$
#[Note][Nota]# In some circumstances, it is helpful to simplify the answer; you should use your best judgment in each situation to decide how much to simplify.