Differentiable curve

A differentiable curve is a mathematical concept referring to a curve that can be described by a differentiable function. In a more formal sense, a curve is said to be differentiable if it is possible to compute its derivative at every point in its domain. For a curve defined in a two-dimensional space, represented by a function \( y = f(x) \), it is differentiable at a point if the derivative \( f'(x) \) exists at that point.