1 The water-soluble vitamins (B vitamins and vitamin C) are absorbed easily along with the water in the small intestine, where they then travel through the body via the blood vessels. 2  Fat-soluble vitamins (vitamins A, D, and K) are absorbed just like the fat mentioned above.
A function f is said to be continuously differentiable if the derivative f'(x) exists and is itself a continuous function. Though the derivative of a differentiable function never has a jump discontinuity, it is possible for the derivative to have an essential discontinuity. For example, the function.
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.