Try applying the rule you came up with in the Warm-up to these functions.

\[\begin{align} y&=(2x-3)(x+2) \\ y&=(2-x)(x+3) \\ y&=(x+3)(1-2x) \\ y&=(3x+4)(2x-5) \\ y&=(3-2x)(5-3x) \end{align}\]
  • Does your original rule give you the correct derivative for these functions?
  • If your original rule works for these functions, can you justify why? If not, then can you adapt your rule to make it work for all of the examples so far?

Does your (new) rule work for \(y=(x^2+3)(x^2+2)\)?

If not, try to adapt it.

Now try it on \(y=(2x^2+3x-2)(x-1)\).

What have you noticed?