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Math Help - easy product rule differentiation

  1. #1
    Senior Member
    Joined
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    easy product rule differentiation

    just need a check to make sure i'm doing this right.

    its just a derivative: cos(cosx)*(-sinx)

    so i would use the product rule.

    is this correct:
    -sin(cosx)(-sinx)*(-sinx) + cos(cosx)*(-cosx)


    thanks for checking.
    if its not correct please fix it, and if it is, maybe help me clean up the negative signs.

    thanks.
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  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
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    South Coast of England
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    Differentiating

    Hello rcmango
    Quote Originally Posted by rcmango View Post
    just need a check to make sure i'm doing this right.

    its just a derivative: cos(cosx)*(-sinx)

    so i would use the product rule.

    is this correct:
    -sin(cosx)(-sinx)*(-sinx) + cos(cosx)*(-cosx)


    thanks for checking.
    if its not correct please fix it, and if it is, maybe help me clean up the negative signs.

    thanks.
    Your working is fine. You can tidy it up a bit to get:

    -\sin(\cos x)\sin^2x-\cos(\cos x)\cos x

    Otherwise there's not much else that will simplify.

    Grandad
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