Question

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

Answer 1

f(x)=(`x^3-4)(3x-3)`
f: `x^3-4,` g: `3x-3`
f':`3x^2` g':`3`
`f'(x)=fg'+gf' =3 (x^3-4)+3x^2(3x-3)`

Explanation:

To find f'(x) I separate the factors into f and g and find the derivative of each of them separately then put it in to the product rule.