![]() We use Differentiation of Vector-Valued Functions and what we know about differentiating functions of one variable. However, because the range of a vector-valued function consists of vectors, the same is true for the range of the derivative of a vector-valued function. The definition of the derivative of a vector-valued function is nearly identical to the definition of a real-valued function of one variable. Now that we have seen what a vector-valued function is and how to take its limit, the next step is to learn how to differentiate a vector-valued function. ![]() However, we will find some interesting new ideas along the way as a result of the vector nature of these functions and the properties of space curves. First, we define the derivative, then we examine applications of the derivative, then we move on to defining integrals. To study the calculus of vector-valued functions, we follow a similar path to the one we took in studying real-valued functions.
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