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.
Historical Examples. 1  The most important theorem in regard to differentiable functions is the âtheorem of intermediate value.â. 2  Particular interest attaches to continuous functions which are not differentiable. 3  Accordingly the function is not differentiable at any point. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3 Various. If the function of x is differentiable, the differential Partial differentiation. Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 5 Various.