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 Pre-Calculus and Calculus
 Vector derivative proof ... with a vector function
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Posted - 01/20/2011 :  23:36:45  Show Profile  Reply with Quote
Hey there, so it has been a while since I have taken Calc, and now I find myself in Calc 3 contemplating my career choices. Needless to say, I need some help proving a simple derivative of a vector-valued function, as I have never dealt with these. Of course I never have time to meet with the teacher when I work all day, so here I am. SO the problem states if |r(t)| > 0 , then show that:
(d/dt)|r(t)| = {(1/|r(t)|)*r(t)} * {(d/dt)r(t)}

What happens as |r(t)|=0 with {(d/dt)r(t)}?

I have never seen a vector function until the other day, and I'm always uncomfortable with the 'prove this' type of general equations.

Thanks in advance for the help!
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3059 Posts

Posted - 01/21/2011 :  12:51:54  Show Profile  Reply with Quote
I believe your second "*" is actually a dot product. Write r(t)=x(t)i+y(t)j+z(t)k and use that.
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Posted - 04/05/2011 :  11:36:55  Show Profile  Reply with Quote

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