What is derivative of f(x)=(2x+1)^2+(2x-2)^2+2(4x^2-2x-2)

We notice that the 3rd term is the result of the product
(2x+1)(2x-2) = (4x^2 - 2x - 2).

If we'll note (2x+1) by a
and (2x-2) by b, and we'll re-write the equation, we'll get a perfect
square:

y=a^2 + 2ab + b^2

y =
(a+b)^2

f(x) = y =
(2x+1+2x-2)^2

We'll combine like
terms:

y = (4x-1)^2

Now, we'll
differentiate both sides, with respect to x:

dy/dx =
2*(4x-1)*(4x-1)'

dy/dx =
2*(4x-1)*4

dy/dx =
8*(4x-1)

We'll remove the
brackets:

dy/dx = 32x -
8

The first derivative of the given function
is f'(x) = 32x - 8.