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Easy differentiation problem

  1. Jul 30, 2012 #1
    f(x)=x^2-3x-3x^-2+5x^-3

    I need help finding the 1st derivative of this function using the power rule.If you can help can you explain how you got the answer.I tried like five times but the differentiation calculator says im getting the wrong answer.heres how o attempted it.

    f(x)'=(2)(x)^2-1 - (3)(x)^1-1 - (3)(-2)(x)^-2-1 + (-3)(5)(x)^-3-1

    here i am applying the power rule to each variable, coefficient and exponent group they each have a different color to help you identify them with the original function.

    f(x)'=2x-3+6x^-3 -15x^-4
    and this is the answer i get

    this is the answer i should get

    f(x)'=(2x^5-3x^4+6x-15)/(x^4)
     
    Last edited: Jul 30, 2012
  2. jcsd
  3. Jul 30, 2012 #2
    ooo colors!
    Notice the edit (in boldface) I have made. Do you see where you went wrong?
     
  4. Jul 30, 2012 #3
    i fixed it.the coefficients are right but the exponents don't match up.
     
  5. Jul 30, 2012 #4
    They do match for me. Can you show what you're getting? (and how you obtain it)
     
  6. Jul 30, 2012 #5

    HallsofIvy

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    The two answers are exactly the same. Just do the indicated division.
     
  7. Jul 30, 2012 #6
    You'll find this more and more in calculus. Your answer and the answer key may look different but still be equivalent.
     
  8. Jul 30, 2012 #7
    I'm sorry i am new to differentiation but how to i do the division?
     
  9. Jul 30, 2012 #8

    Mark44

    Staff: Mentor

    You don't actually have to do any division. Multiply the numerator by x4 and multiply the denominator by x4. In other words, you're multiplying your answer by 1, to get rid of the negative exponents in the numerator.
     
  10. Jul 30, 2012 #9
    It worked thanks :).but why do you multiply by x^4 instead of X^3 or something like that?
     
  11. Jul 30, 2012 #10

    SammyS

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    ... because you have an x-4 in you expression for the derivative.
     
  12. Jul 30, 2012 #11
    Also because there is an x4 in the denominator in the answer. ;)
     
  13. Jul 31, 2012 #12

    Mark44

    Staff: Mentor

    The only reason for multiplying by x4 over itself is because of the x-4 term in the numerator. The x4 is a result of this multiplication, not the reason for it.
     
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