2.45. CHAPTER 2, PROBLEM 451292.45Chapter 2, Problem 45Problem:Consider the vectorsA=ti+2t2j−tkandB=i+tj+t2k. Compute the first derivativeofA·Bwith respect to time by forming the dot product and differentiating. Verify that the chain rulefor a dot product [Equation (2.37)] yields the same derivative.Solution:The dot product ofAandBisA·B=tt3−t3=t+t3Differentiation with respect totyieldsddt(A·B)=1+3t2To check for consistency with the chain rule, note that
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