@Kitonum 

Thank you so much. This was exactly the sort of thing i hoped for <3

@Carl Love 

I was told by my instructor of the Calculus alpha course I'm attending that both of the solutions were wrong. At first I was suspicious too, but then I checked the equivalence of "my" correct solution with the ones given by maple with an is() statemet and got "false". Furthermore I checked in TI-Nspire as well. To me that suggest that it would be improper to not stand by my instructor's authority. 

And I thought it would be clear to anybody, espcially math teachers, that my "proof" was not supposed to by strict in any (mathematical) way.