13.2 Derivatives and Integrals of Vector FunctionsThe derivative of a vector function (), ()tftgtht=ris '',', 'tgtht=r. Note that you differentiate each component separately. For example, look at the 2-dimensional space curve defined by 4sin, 2costt=−tr. If ris the position function of a particle, then ris the velocity function, like the velocity function in one dimension. t'( )tLet's look at a geometric description of the derivative r. The derivative ris tangent to the space curve r. ttt-2-112-0.50.51The figure shown above is the curve 2s,cosrtwith the derivative vector 2 cos( ),
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This note was uploaded on 01/20/2012 for the course MATH 2057 taught by Professor Estrada during the Fall '08 term at LSU.