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Trying to differentiate using function of a function/Chain rule

  1. Jun 24, 2014 #1
    1. The problem statement, all variables and given/known data

    Using the function of a function formula differentiate the following:

    y = (cos 2x)3

    2. Relevant equations

    dy/dx = dy/du * du/dx

    3. The attempt at a solution

    y = (cos 2x)3

    u = cos 2x
    y = u3

    dy/du = -2sin2x
    du/dy = 3u2

    dy/dx = dy/du * du/dx

    dy/dx = -2sin2x * 3(cos2 2x)

    = -6sin2x cos22x

    Hi, I've been racking my brain over this question for sometime now, I've attempted it multiple times getting it wrong over and over again. I've got this answer, but, I'm really not confident that it is right. Can you guys take a look at it and work some magic? It's function of a function, which I think is more commonly known as the Chain rule.

    Thank you.
  2. jcsd
  3. Jun 24, 2014 #2


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    Science Advisor
    Gold Member

    That looks right to me.
  4. Jun 24, 2014 #3

    I'm speechless!
  5. Jun 24, 2014 #4
    should read as:
    [tex]\frac{dy}{du} = 3u^2[/tex] and
    [tex]\frac{du}{dx} = -2\sin 2x[/tex]
    but other than that, it looks fine.
  6. Jun 25, 2014 #5
    Haha, there's my attention to detail. Thanks very much, guys, I can finally lay this to rest.
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