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Homework Help: This one is a bit easier

  1. Mar 28, 2005 #1
    OK, in Calculus, in finding the derivative of y=(1+cos²7x)³ my textbook says the answer is -42(1+cos²7x)²cos7xsin7x. Where did they get the cos7x from?
     
  2. jcsd
  3. Mar 28, 2005 #2

    Doc Al

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    Hint: What's the derivative of [itex]cos^2(7x)[/itex] ?
     
  4. Mar 28, 2005 #3

    dextercioby

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    What is the derivative of

    [tex] 1+\cos^{2}7x [/tex]

    ?

    Daniel.
     
  5. Mar 28, 2005 #4

    chroot

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    The derivative of

    [tex]\left( 1 + \cos^2 7x \right) ^3[/tex]

    is

    [tex]3 \cdot \left( 1 + \cos^2 7x \right) ^2[/tex]

    ...times the derivative of the stuff inside the ^3, which is

    [tex]2 \cdot \cos 7x[/tex]

    ...times the derivative of the stuff inside the ^2, which is

    [tex]-\sin 7x[/tex]

    ...times the derivative of the stuff inside the sin, which is 7.

    So, in total, we have

    [tex]3 \cdot \left( 1 + \cos^2 7x \right) ^2 \cdot 2 \cdot \cos 7x \cdot -\sin 7x \cdot 7[/tex]

    which reduces to the answer you've been shown.

    - Warren
     
  6. Mar 28, 2005 #5

    dextercioby

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    I think Warren started writing his post ahead of us,Doc.:smile:

    Daniel.
     
  7. Mar 28, 2005 #6
    Alright, I think I was just overlooking a few things. Thank-you all for pointing me in the right direction.
     
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