Derivative for Vector Functions by Components + Proof

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2025-09-20 03:40

In this video I show that the derivative of a vector function is equal to the derivative of the real-valued functions in its components. I prove this by applying the definition of derivatives for vector functions, and then apply basic limit and vector laws to obtain the corresponding definition of derivative of each real-valued function in each component. This is a straight forward proof, and the result means that to obtain the derivative of a vector function, we just take the derivative of it components!

#math #science #calculus #vectorfunctions #proof

2 Derivative by Components.jpeg

Timestamps

Theorem: Derivative of Vector Functions by Components: 0:00
Proof: Using Definition of Derivative of Vector Functions: 1:26
Definition of Derivative of real-valued functions in each component of the vector function: 6:04
Derivative is just the derivative of components of the vector function: 7:08