Definition: Derivative of an n-Dimensional Curve

Let \(I\) be a real interval and \(V\subseteq\mathbb R^n\) be an \(n\)-dimenstional euclidean vector space. An \(n\)-dimensional curve \(f\colon I\longrightarrow V\,\) is called differentiable at \(t\in I\), if the limit. \[\operatorname {lim} _{h\rightarrow 0}\,{\frac {f(t+h)-f(t)}{h}}\]

exists. If \(f\) is differentiable at every \(t\in I\), then we call the limit the derivative of \(f\) and is denote it by \(f'(t)\).

Definitions: 1

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Adapted from CC BY-SA 3.0 Sources:

  1. Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück