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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.

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3 Answers 3

Your answer is correct...the source answer is incorrect.

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Thank you sir, I almost blew my mind trying to understand this. –  Luan Cristian Thums Mar 1 '13 at 17:52
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I have caught many errors in calculus and other math books. Practice will make you solid, however, always triple check your work (I made mistakes copying problems incorrectly, things like that are frustrating). Make sure that your answer makes sense. –  Vic Mar 1 '13 at 17:58

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.

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Thank you for your answer! It's from Khan Academy. I would not have fully trusted the answers from there because are users from the academy that make the questions (at least I think so) but all the answers are like that so I thought i should be mistaken. –  Luan Cristian Thums Mar 1 '13 at 17:56
    
You're welcome! –  amWhy Mar 1 '13 at 17:57
    
What is the meaning of fret? I didn't see it before + –  Babak S. Mar 2 '13 at 16:51
    
@Babak "Do not fret" $\equiv$ "do not worry" –  amWhy Mar 2 '13 at 16:57

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.

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