Derivatives of Vector-Valued Functions | Calculus 3 Lesson 26 - JK Math

How to Find Derivatives of Vector-Valued Functions (Calculus 3 Lesson 26)

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In this video you will learn about how to find derivatives of vector-valued functions. This includes seeing the limit definition of the derivative for vector functions and how it can be simplified to a nice formula for finding the derivative of a vector function (taking the derivative of each component). We then look at examples of taking the first and second derivatives of some vector functions. Also, we learn the properties for the derivatives of vector functions.

This video series is designed to help students understand the concepts of Calculus 3 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!

Calculus 3 requires a solid understanding of concepts from calculus 2, calculus 1, precalculus, and algebra. This includes limits, differentiation, advanced integration techniques, applications of derivatives and integrals, polar coordinates, parametric equations, trigonometric functions, logarithms, factoring, equation manipulation, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!


Video Chapters:
0:00 Derivative Definition Review
3:05 Limit Definition of the Derivative of Vector Functions
10:42 Finding the Shortcut Method
17:22 Summary of Formulas
19:12 Example: 1st & 2nd Derivatives of〈t^3, t², t〉
21:44 Example: 1st & 2nd Derivatives of〈ln(t), e^t, √t 〉
25:26 Example: Derivative of〈sin²(t), e^t*cos(t), arcsin(t)〉
29:51 Derivative Properties for Vector Functions
37:44 Example: Using a Derivative Property


📝 Examples Video:    • Derivatives of Vector-Valued Functions Exa...  

⏩ Next Lesson:    • Tangent Vectors | Calculus 3 Lesson 27 - J...  

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📺 Calculus 1 Playlist:    • Calculus 1  


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