How would you differentiate f(x)=3x(2x-1)^2

This question is really straight forward

By using the Chain rule: f'(x) = uv' + u'v.

let u=3x, so u'=3

let v=(2x-1)^2, so v'=2x2(2x-1)=8x-4

Now, we put this expression altogether:

As f'(x) = uv' + u'v

f'(x)=3x(8x-4)+3(2x-1)^2

f'(x)=24x^2-12x+12x^2+3-12x

And now, simplify

f'(x)=36x^2-24x+3