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In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.
CHAPTER I. ELEMENTARY DIFFERENTIAL GEOMETRY. Â§1-Â§3. When a Euclidean space is stripped of its vector space structure and. only its differentiable structure retained, there are many ways of piecing together. domains of it in a smooth manner, thereby obtaining a so-called differentiable. manifold.