On differentiation of vector-valued functions
This important result is listed in the theorem on the next page. Note that the derivative of the vector-valued function is itself a vector-valued function. You can see from Figure 12.8 that is a vector tangent to the curve given by and pointing in the direction of increasing values. tr t r t r f t i g t j lim t→0 f t t f t t i lim t→0 g t t g t t j lim t→0 f t t f t t i g t t g t t j lim t→0 f t t i g t t j f t i g t j t r t lim t→0 r t t r t t r t f t i g t j. dr dt . Dt r t , d dt r t , r t ,