Derivative of this function using the Power Rule I'm studying calculus on my own until my classes starts in May (Computer engineering) and I have one doubt. The following function:
$$f(x)=5x^{3}-2x^{2}-3x-5-7x^{-1}-1-2x^{-2}$$
I applied  the power rule to it and I got: 
$$f'(x)=15x^{2}-4x-3+7x^{-2}+4x^{-3}$$
But the answer of the question says that the correct is:
$$f'(x)=15x^{2}-4x-3$$
Can someone explain to me why is that all the x's to the negative power become 0 applying the power rule? Sorry for the noob question and for the links, I can't post images here because that's my first question.
 A: Your answer is correct...the source answer is incorrect.
A: Do not fret, your answer is correct. Don't second-guess your work: you did very well, (and no, the power rule applied to terms with negative exponents does not make them $0$!
As a rule, solution manuals/solutions in the appendices of books are less carefully edited than are the problems or text themselves. (Solutions are often not authored by the author of the text/exercises themselves, and proof-readers/publishers, etc. don't usually have the expertise to check for "correctness".) This can be terribly aggravating, because such errors are typically not discovered until students/instructors encounter discrepancies, like you yourself encountered.  
Check to see of your text/solution manual has an "Errata" page on line (Google "text title": Errata). Those are more easily compiled and published these days with the availability of doing so on the web, on-going-as-discovered.
ADDED: Since you encountered this through Khan Adademy, I suspect there's a "contact" link somewhere on site where users can offer feedback and/or report errors. I'm sure there are folks "in charge" of creating/compiling/maintaining exercises and (correct, when possible!) solutions.
A: It seems as if the source answer disregarded the last two terms in your function $f$. Your answer is correct. Maybe you should check that you didn't see some part of the answer. 
