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Homework Help: Taking the derivative of a function (looks easy but I don't know how to do it)

  1. Jan 17, 2012 #1
    1. The problem statement, all variables and given/known data
    f(x) = x(x-5)^4

    2. Relevant equations

    3. The attempt at a solution
    I used product rule and chain rule so,
    1(x-5)^4 + 4x(x-5)^3(1)

    The answer to this question is 5(x-5)^3(x-1). I left it like the answer above. I don't know how to expand (x-5)^4. Thanks.
  2. jcsd
  3. Jan 17, 2012 #2
    Your differentiation looks right. Just factorise out the [itex](x-5)^3[/itex] and you should be able to get it in that form.
  4. Jan 17, 2012 #3


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    Science Advisor
    Homework Helper

    Don't expand (x-5)^4. Factor (x-5)^3 out of both terms of your answer and collect what's left.
  5. Jan 17, 2012 #4


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    Gold Member

    No expansion is necessary, simply rewrite it as [itex](x-5)(x-5)^3[/itex]. Then you'll have a term [itex]x(x-5)^3[/itex] and [itex] -5(x-5)^3[/itex].
  6. Jan 17, 2012 #5
    haha. Why didn't I see that? Thanks guys.
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