13.2 Derivatives and Integrals of Vector FunctionsThe derivative of a vector function ( )( ),( ), ( )tf tg th t=ris '( )'( ),'( ),'( )tftgth t=r. Note that you differentiate each component separately. For example, look at the 2-dimensional space curve defined by ( )4sin( ),2cos( )tt=−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. '( )t'( )t( )t-2-112-1-0.50.51The figure shown above is the curve ( )2sin( ),cos( )
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