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Section 12.7 : Calculus with Vector Functions
4. Compute the derivative of the following limit.
\[\vec r\left( t \right) = \left( {{t^3} - 1} \right)\vec i + {{\bf{e}}^{2t}}\,\vec j + \cos \left( t \right)\vec k\] Show SolutionThere really isn’t a lot to do here with this problem. All we need to do is take the derivative of all the components of the vector.
\[\require{bbox} \bbox[2pt,border:1px solid black]{{\vec r'\left( t \right) = 3{t^2}\vec i + 2{{\bf{e}}^{2t}}\,\vec j - \sin \left( t \right)\vec k}}\]