Introduction Biopharmaceutics history 2

Differential Calculus
Differential calculus is a branch of calculus that involves finding the rate at which a variable quantity is changing. For example, a specific amount of drug X is placed in a beaker of water to dissolve. The rate at which the drug dissolves is determined by the rate of drug diffusing away from the surface of the solid drug and is expressed by the Noyes–Whitney equation:
= dX = −dtDA Dissolution rate l (C1 C2 )
where d denotes a very small change; X = drug X; t = time; D = diffusion coefficient; A = effective surface area of drug; l = length of diffusion layer; C1 = surface concentration of drug in the diffusion layer; and C2 = concentration of drug in the bulk solution.
The derivative dX/dt may be interpreted as a change in X (or a derivative of X) with respect to a change in t.
In pharmacokinetics, the amount or concentration of drug in the body is a variable quantity (dependent variable), and time is considered to be an independent variable. Thus, we consider the amount or concentration of drug to vary with respect to time.
EXAMPLE
The concentration C of a drug changes as a function of time t:
C =f(t) (2.1)
Consider the following data:

Time (hours)	Plasma Concentration of Drug C (μg/mL)
0	12
1	10
2	8
3	6
4	4
5	2

The concentration of drug C in the plasma is declining by 2 mg/mL for each hour of time. The rate of change in the concentration of the drug with respect to time (ie, the derivative of C ) may be expressed as dc = µdt 2 g/mL/h

Here, f(t) is a mathematical equation that describes how C changes, expressed asC =12− 2t