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Product and chain rule

  1. Feb 9, 2007 #1
    i am having trouble with this one problem. maybe you can tell me where i am going wrong.

    find h'(t) if h(t)=(t^6-1)^5(t^5+1)^6

    so i am using product rule and to find the derivatives of each expression i am using chain rule...

    so i get h'(t)=30t^4(t^6-1)^4(t^5+1)^6+30^4(t^5+1)^5(t^6-1)^5


    is that right..or what is wrong with it?
     
  2. jcsd
  3. Feb 9, 2007 #2

    D H

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    Not quite right. The factors [itex](t^6-1)^4(t^5+1)^6[/itex] and [itex](t^5+1)^5(t^6-1)^5[/itex] in the two terms are correct, but the factors involving a power of [itex]t[/itex] are not.

    What is [itex]\frac d{dt}\left((t^6-1)^5\right)[/itex] ?
     
  4. Feb 9, 2007 #3

    HallsofIvy

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    The derivative of (t6-1)5 is 5(t6-1)4(6t5= 30t5(t6-1)4. I think you've missed a power of t in the first term above.

    The derivative of (t5+ 1)6 is 6(t5+ 1)5(5t4)= 30t4(t5+ 1)5
    You seem to be missing a "t"! (30^4 instead of 30t^4!)
     
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