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Thread: Derivative of Vector-Valued Function

  1. #1
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    Derivative of Vector-Valued Function

    Find the derivative of the vector-valued function below.

    r (t) = i + j + k

    Is the answer r'(t) = 1 + 1 + 1 or 3?

    Note: There is no letter t in front of i, j and k. Do we assume there is a number 1 there for all three letters?
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  2. #2
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    Re: Derivative of Vector-Valued Function

    I don't understand how you can do the other problems but get this one so wrong.

    $r(t) = (1,1,1)$

    $\dfrac {d}{dt}(1) = 0$

    $r^\prime(t) = (0,0,0)$

    the derivative of a vector valued function will be a vector
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    Re: Derivative of Vector-Valued Function

    Quote Originally Posted by romsek View Post
    I don't understand how you can do the other problems but get this one so wrong.

    $r(t) = (1,1,1)$

    $\dfrac {d}{dt}(1) = 0$

    $r^\prime(t) = (0,0,0)$

    the derivative of a vector valued function will be a vector
    I also don't get it. I find myself able to process through a complex problem but easily get lost or confused with simple questions not only in calculus but in courses before calculus.
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  4. #4
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    Re: Derivative of Vector-Valued Function

    I broke it down this way:

    i = 1*i...The derivative of 1 is 0. Thus, we get 0i and 0 times anything is 0. The same can be done with j and k.
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  5. #5
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    Re: Derivative of Vector-Valued Function

    Because you are memorizing formulas and methods rather than learning mathematics! If you understood the concepts behind the formulas and methods, you would have immediately realized that this vector function is a constant and the derivative of any constant is 0. The same problem showed up with the previous problem, finding the tangent and normal vectors to a curve that was, actually, the x-axis!
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