Find Y' when Y= X^(2)e^(cos2x)

$\displaystyle Y= X^2e^{cos2x}$

These are the steps my teacher wrote down on the board. She used the Product rule.

a) Y'=[{X^(2)}'*{e^(cos2x)}]+[{X^(2)}*{e^(cos2x)}']b) Y' = 2Xe^(cos2x) +

X^(2)e^(cos2x)* [1-2sin(2x)]

c) Y' = 2Xe^(cos2x)[-2sin(2x)]1

So my questions are.

1) Where did that1come from?

2) How to go from step b to step c. Especifically why didX^(2)e^(cos2x)disapear in the final answer.