Math Help - Could someone verify this derivation for me?

1. Could someone verify this derivation for me?

$y = e^{2x}(1 - x)$
$y = e^{2x} - xe^{2x}$
$y^{'} = 2e^{2x} - 2xe^{2x} + e^{2x}$
$y^{'} = 3e^{2x} - 2xe^{2x}$

It's part of a larger question, so there's no solution in my textbook that I can check with. Thank you.

2. Originally Posted by Glitch
$y = e^{2x}(1 - x)$
$y = e^{2x} - xe^{2x}$
$y^{'} = 2e^{2x} - 2xe^{2x} + e^{2x}$
$y^{'} = 3e^{2x} - 2xe^{2x}$

It's part of a larger question, so there's no solution in my textbook that I can check with. Thank you.
That is correct, I'd write it as:

$y^{'} = e^{2x}(3 - 2x)$

3. Indeed, that is neater. Thanks!

4. Your derivative is incorrect here. You forgot that the minus sign also applies to the third term in the first line where you take the derivative. That is,

$y' = 2e^{2x} - 2xe^{2x} - e^{2x}.$

This will impact, possibly, your other post.