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Re: need a help again,

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  • sara2_ch
    ... ????????????????????????????????????????? u mean there isnt any diferent between the first derivative & the nth derivative of (sinx)^a?!?! that one that u
    Message 1 of 5 , Apr 13, 2002
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      --- In mathforfun@y..., slim_the_dude <no_reply@y...> wrote:
      > > is there any formula for nth derivative of (sinx)^a?(with proof)
      >
      > I assume you mean with respect to x, with a held constant.
      >
      > Using the power rule, d/dx (sinx)^a =
      >
      > [a * (sinx)^(a-1)]*d/dx sinx =
      > a*cosx*(sinx)^(a-1)


      ?????????????????????????????????????????
      u mean there isnt any diferent between the first derivative & the nth
      derivative of (sinx)^a?!?!
      that one that u said is just for the first derivative,
    • slim_the_dude
      Message 2 of 5 , Apr 15, 2002
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        << u mean there isnt any diferent between the first derivative & the
        nth
        derivative of (sinx)^a?!?!
        that one that u said is just for the first derivative, >>

        Oops... I totally missed the part where you're asking for the nth
        derivative. Let me modify
        my answer then:

        First, note that for f(x) = (sinx)^a, we have:

        f'(x) = a*cosx*(sinx)^(a-1)
        f''(x) = a^2*(cosx)^2*(sinx)^(a-2) - a*(sinx)^a
        f(3)(x) = a^3*(cosx)^3*(sinx)^(a-3) + 2 a^2 * cosx sinx - a^2 cosx*
        (sinx)^(a-1)

        ...

        I'm having trouble finding the pattern, so sorry, I don't have your
        answer.
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