Derivatives & Integrals of Vectors

AP Calculus · Axiom Academy

LESSON Derivatives & Integrals of Vectors Calculus with vector-valued functions Step 1: Derivatives of Vector Functions Taking the derivative of a vector-valued function is straightforward: differentiate each component! That's it! The derivative is computed component-by-component, just like any regular derivative. Step 2: Integrals of Vector Functions Integrating vector-valued functions is also done component-by-component: Again, this is straightforward: integrate each component. Don't forget the constant of integration (which is now a vector)! Step 3: Geometric Interpretation The derivative has special geometric meaning: Step 4: Important Calculus Rules The usual calculus rules apply to vector functions:

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