Question

how do i find the first derivative of w= (z+1)(z-1)(z^2+1). do i use the product formula?

Answer 1

easier way is to multiply them out

Answer 2

This problem is setup to simplify really nicely :)
Multiplying it out will work out really well.

Notice that the first 2 terms are exactly the same, except with a different sign between them?
Each term is the conjugate of the other!
When you multiply conjugates, you get the difference of squares.
Example:
\[(a-b)(a+b)=(a^2-b^2)\]

If you're able to get through that step, look at it afterwards, you might notice that have conjugates again ;)
Fun little problem :D