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.
It is is not differentiable at x = 0. Let |z| be an absolute value function of which we have to find the derivative, Recall that |z| = $\sqrt{Z^2}$. By using this we can find the derivative of |z|, $\frac{d}{dz}$ |Z| = $\frac{d}{dz}$ $\sqrt{Z^2}$. = $\frac{d}{dz}$ $(Z^2)^{\frac{1}{2}}$.