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Math Help - Strange differential problem?

  1. #1
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    Strange differential problem?

    Find the differential dy of the given function

    y= (1/3) cos((6pi times x-1))/((2))

    Can anyone help me with this problem?
    Last edited by homeylova223; August 4th 2011 at 02:28 PM.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Strange differential problem?

    There's no variable x in the given function, so that means ...
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    Re: Strange differential problem?

    modify
    Last edited by homeylova223; August 4th 2011 at 02:10 PM.
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Strange differential problem?

    That means you're taking the differential of a constant number, and what's the differential of a constant number?
    (in general: dy=f'(x)\cdot dx)
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    Re: Strange differential problem?

    Actually I have to admit I made a typo

    y= (1/3) cos((6pi x-1))/((2)) is how it is correctly written

    I am sorry...
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Strange differential problem?

    Do you know the chain rule? But write:
    y=\frac{1}{3}\cdot \left[\frac{\cos(6\pi (x-1))}{2}\right]=\frac{1}{6}\cdot \left[\cos(6\pi (x-1))\right]

    But it's still not clear, you have to be more clear with: \cos(6\pi(x-1)) or \cos(6\pi\cdot x-1)?
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  7. #7
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    Re: Strange differential problem?

    No in my textbook the problem is written

    ((1/3)) cos ((6pi times x-1))/((2))

    The cos is outside the parenthesis

    It can be tough being clear sometimes.
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  8. #8
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    Re: Strange differential problem?

    Either way you'll have to use the chain rule for this one.
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  9. #9
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    Re: Strange differential problem?

    Quote Originally Posted by homeylova223 View Post
    No in my textbook the problem is written

    ((1/3)) cos ((6pi times x-1))/((2))

    The cos is outside the parenthesis

    It can be tough being clear sometimes.
    is this it?

    y = \frac{1}{3} \cos\left(\frac{6\pi x - 1}{2}\right)

    you really need to learn Latex ...
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  10. #10
    MHF Contributor Siron's Avatar
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    Re: Strange differential problem?

    Modified
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    Re: Strange differential problem?

    Yes skeeter is correct.

    I have to apply the chain rule.

    Can anyone show me the first step?
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  12. #12
    MHF Contributor Siron's Avatar
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    Re: Strange differential problem?

    If you want to use the chain rule here:
    D\left[\cos\left(\frac{6\pi x-1}{2}\right)\right]=-\sin\left(\frac{6\pi x-1}{2}\right)\cdot D\left(\frac{6\pi x-1}{2}\right). Can you go further? You don't have to use the quotienrule, just put \frac{1}{2} outside, because it's a constant.
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  13. #13
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    Re: Strange differential problem?

    Alright following Siron adivce


    -sin((6pi times x-1))/((2)) times cos(6pi)(-1/2)

    would this be correct?
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  14. #14
    MHF Contributor Siron's Avatar
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    Re: Strange differential problem?

    That's not correct, it has to be:
    D\left(\frac{6\pi x-1}{2}\right)=\frac{1}{2}\cdot D\left(6\pi x-1\right)=\frac{1}{2}\cdot 6\pi=3\pi

    Can you now finish the differential of the given function.
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  15. #15
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    Re: Strange differential problem?

    y = \frac{1}{3} \cos\left(3\pi x - \frac{1}{2}\right)

    \frac{dy}{dx} = -\frac{1}{3} \sin\left(3\pi x - \frac{1}{2}\right) \cdot 3\pi

    \frac{dy}{dx} = -\pi \sin\left(3\pi x - \frac{1}{2}\right)
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