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Section 12.7 : Calculus with Vector Functions
5. Compute the derivative of the following limit.
\[\vec r\left( t \right) = \left\langle {\ln \left( {{t^2} + 1} \right),t{{\bf{e}}^{ - t}},4} \right\rangle \] 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.
\[\require{bbox} \bbox[2pt,border:1px solid black]{{\vec r'\left( t \right) = \left\langle {\frac{{2t}}{{{t^2} + 1}},{{\bf{e}}^{ - t}} - t{{\bf{e}}^{ - t}},0} \right\rangle }}\]Make sure you haven’t forgotten your basic differentiation formulas such as the chain rule (the first term) and the product rule (the second term).