The problem seems to be to take the derivative of , for which the correct solution is . That's e times in parentheses.
I don't follow your solution starting at the second line - it looks like it should be (not ), and I don't get the stuff in brackets at all.
The solution to this derivative is pretty straightforward - just use the chain rule and work from the outside in:
: the derivative of is , so use the chain rule
: bring out the constant e and cancel
: the derivative of is , so use the chain rule
: the derivative of is
- Hollywood