# How do you differentiate f(x)=x^3(4x - 12) using the product rule?

Dec 14, 2015

Product Rule:
If we have two functions $f \left(x\right)$ and $g \left(x\right)$, then
$\frac{d}{\mathrm{dx}}$ $f \left(x\right) g \left(x\right)$ = ${f}^{'} \left(x\right) g \left(x\right) + f \left(x\right) {g}^{'} \left(x\right)$

Original Equation:
$f \left(x\right) = {x}^{3} \left(4 x - 12\right)$

The two equations you're multiplying are ${x}^{3}$ and $\left(4 x - 12\right)$

Take the derivative of the first equation (${x}^{3}$) and times it by the second equation ($\left(4 x - 12\right)$)

You should get (3x^2)•(4x-12)

Next, take the derivative of the second equation ($\left(4 x - 12\right)$) and times it by the first (${x}^{3}$).

You should get (x^3)•(4)

You should get ((3x^2)•(4x-12) )+ ((x^3)•(4))
Your final answer should be $16 {x}^{3} - 36 {x}^{2}$