Differentiating a vector-valued function involves finding the derivative of each component of the vector separately. It measures how the vector changes with respect to its independent variable.
Think of a group of friends walking together in a park. Each friend represents a component of the vector, and differentiating the vector-valued function is like observing how each friend's position changes as they walk.
Tangent Vector: A tangent vector represents the instantaneous rate of change or velocity at any given point on a curve.
Chain Rule for Vector-Valued Functions: The chain rule allows us to find derivatives of composite functions involving vectors.
Parametric Equations: Parametric equations describe curves by expressing coordinates as functions of an independent parameter.
Study guides for the entire semester
200k practice questions
Glossary of 50k key terms - memorize important vocab
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.