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Math Help - find derivative of a trig function (chain rule included)

  1. #1
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    find derivative of a trig function (chain rule included)

    Just trying to verify my work.
    Find dy/dx for y=sin^5(cos(cos(3x)))

    dy/dx= 5(sin(cos(cos(3x))))^4 * cos(cos(3x)) * (-sin(3x)) * 3

    Does this look right to you all?
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  2. #2
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    I get

    \displaystyle \frac{dy}{dx} = 5\sin^4(\cos (\cos 3x)) \times 3\cos (\cos 3x) \times \sin 3x \times \sin (\cos 3x)
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  3. #3
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    I don't follow this answer at all, Pickslides. Can you explain the steps you followed????
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  4. #4
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    reasoning

    dy/dx of y=sin^5(cos(cos3x)) which is also (sin(cos(cos(3x)))^5

    Logically, we multiply the entire function by the exponent (5) and reduce it (the exponent) by 1.

    y=5(sin^4(cos(cos(3x)))

    Then we move along to the second layer (sin(cos(cos(3x))) which gives us

    y=5(sin^4(cos(cos(3x))) * cos(cos(3x))

    Then the third layer (cos(3x))

    y=5(sin^4(cos(cos(3x))) * cos(cos(3x)) * (-sin(3x))

    Then the fourth layer (3x)

    y=5(sin^4(cos(cos(3x))) * cos(cos(3x)) * (-sin(3x)) * 3

    It would help me greatly if you could point out the specific flaws in this logic. Thanks so much!
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  5. #5
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    Take a look at this.

    Be sure to ask it to show steps.
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  6. #6
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    So now we have 3 answers... hahaha. And no explanations. Sad-face.jpg
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  7. #7
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    Quote Originally Posted by AlphaTauLambda View Post
    So now we have 3 answers... hahaha. And no explanations. Sad-face.jpg
    But you have only one correct answer.
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  8. #8
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    mistyped equation - trig function with chain rule

    find dy/dx of sin^5(cos(3x))

    I have, 5sin^4(cos(3x)) * cos(cos(3x)) * (-sin3x) * 3

    Moderator edit: User made this correction to the original question that was asked.
    Last edited by Chris L T521; May 8th 2011 at 04:23 PM.
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  9. #9
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by AlphaTauLambda View Post
    find dy/dx of sin^5(cos(3x))

    I have, 5sin^4(cos(3x)) * cos(cos(3x)) * (-sin3x) * 3
    Which looks good to me!
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  10. #10
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    Quote Originally Posted by Chris L T521 View Post
    Which looks good to me!
    It may look good to you, but it is wrong.
    This is the correct answer.
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  11. #11
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Plato View Post
    It may look good to you, but it is wrong.
    This is the correct answer.
    I agree that's the correct answer to what the user originally posted. However, they created a new thread with a "corrected" version (which I happened to merge into this one). So my comment was directed to the post which had the "fixed" version of the question.
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