Why Can't I Cancel e^x in this Expression?

[AFG34]

[SOLVED] Why can't i cancel this term?

http://tinypic.com/view.php?pic=2jcc49l&s=4
The function g(x) is stated in the first line.
The question asks for g' when x=0

In the third line, i canceled e^x from both terms in the expression. The TA wrote that i can't do that. I forgot to ask him and now i need to know why.

Thanks

 

[lurflurf]

It was not wrong to cancel, but you canceled wrong.
you had (e^x)(e^x)/e^x
then e^x
then 1
where did the other e^x go?
as an aside
g=exp(x)log3(e^x)
why no try
g=exp(x)log(e^x)/log(3)=x exp(x)/log(3)
to start and avoid the other problems?

 

[Hurkyl]

When reviewing your mistakes, it's not enough to ask why you were wrong -- you also have to ask yourself why you thought you were right.

So, why did you think you were right?

 

[AFG34]

Looked at it again and found my mistake...one of those "stupid" mistakes. I thought i was right because i thought it was legal to cancel e^x..maybe i was going too fast or i wasn't concentrating enough due to sleep deprivation.

Thanks for your replies.

btw, funny comic in your sig Hurkyl. Once my math teacher told us that the reason he chose to teach math is because you're either right or wrong...no in between.