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 \(f'(t)\).
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