Name: Differentiation Rules for Vector Functions
Uploaded: 2025-10-02T02:55:12+00:00
Duration: 7 min 18 s
Description: In this video I go over the six main differentiation rules for vector functions, as well as the 2nd (or higher) derivatives. The rules have their similar counterparts for real valued functions, and I

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In this video I go over the six main differentiation rules for vector functions, as well as the 2nd (or higher) derivatives. The rules have their similar counterparts for real valued functions, and I leave the proofs for later videos. Deriving each rule involves either applying the definition of a derivative for a vector function or applying the theorem of differentiating functions by components.

#math #science #calculus #vectors #education

Timestamps:

- Second derivative of a vector function is just the derivative of the derivative: 0:00
- Differentiation rules have counterparts for real-valued functions: 1:48
- Formula 1: Derivative of Addition of Vector functions: 2:20
- Formula 2: Constant multiple: 3:00
- Formula 3: Real-valued function multiple: 3:27
- Formula 4: Dot product: 4:15
- Formula 5: Cross product: 5:08
- Formula 6: Chain rule: 5:50
- Screenshot of the 6 differentiation rules from my Calculus Book: 6:50