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Homework Help: Strange derivative problem

  1. Oct 18, 2009 #1
    1. The problem statement, all variables and given/known data
    [tex]f(t)=\frac{t^5 + t^6 - 1}{t^7}[/tex]

    2. Relevant equations

    3. The attempt at a solution
    This is different than the other problems I've been doing.

    My first guess would be that I would do this:
    [tex]f(t)=\frac{5t^4 + 6t^5}{7t^6}[/tex]
    Is that the final answer or is there another step I need to do?
  2. jcsd
  3. Oct 18, 2009 #2


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  4. Oct 18, 2009 #3


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    Science Advisor
    Homework Helper

    Or simply write it as the sum

    t^-2 + t^-1 - t^-7
  5. Oct 18, 2009 #4
    Hey, thanks that was really helpful! I didn't think of dividing by t^7.

    That made it easy! Thank you! I'll remember this if I get another similar problem!
  6. Oct 19, 2009 #5


    Staff: Mentor

    As already noted, this is wrong. If you carried out this differentiation without simplifying first, you would need to use the quotient rule. whs has already provided a link to an article on differentiation rules, so I won't give that link again. The upshot is that if f(x) = g(x)/h(x), f'(x) is NOT equal to g'(x)/h'(x), which is precisely what you did.
  7. Oct 19, 2009 #6
    U must use quotient Rule!
  8. Oct 19, 2009 #7


    Staff: Mentor

    That's not necessary in this problem. As nicksauce already suggested, the OP can carry out the division and then use the sum rule and the power rule.
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