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Math Help - find derivative of this equation

  1. #1
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    find derivative of this equation

    This question may not belong here but it is a simple derivative question including vectors.

    \vec{r} = a\sin(\omega t) \hat{x} + b\cos(\omega t) \hat{y}; \:\:\: \hat{x}, \hat{y} are unit vectors

    (\vec{r})^\prime = ?

    I have a couple questions:

    1) is the derivative of sin(wt), cos(wt), or do I do something extra with the angle in the parenthesis?
    2) is the unit vector x considered a function? and if so what is it's derivative? I would assume \hat{x}^\prime = 1
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  2. #2
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    e^(i*pi)'s Avatar
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    You do need to use the chain rule \dfrac{d}{dt} \cos(\omega t) = -\omega \sin(\omega t)

    Unfortunately, I do not know vector calculus
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  3. #3
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    thanks!

    But I have no idea what to do with the unit vector x?

    Can someone please help?
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  4. #4
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    Quote Originally Posted by jayshizwiz View Post
    thanks!

    But I have no idea what to do with the unit vector x?

    Can someone please help?
    It depends on how the unit vectors are defined as to whether or not you differentiate them. eg. The unit vectors i, j, k do not get differentiated. If the direction of your unit vectors does not change with time, then you only differentiate the components. I'm sure your textbook or class notes will have examples to follow.
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