Logarithmic differentiationIn calculus, logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic derivative of a function f, The technique is often performed in cases where it is easier to differentiate the logarithm of a function rather than the function itself. This usually occurs in cases where the function of interest is composed of a product of a number of parts, so that a logarithmic transformation will turn it into a sum of separate parts (which is much easier to differentiate).
Rate (mathematics)In mathematics, a rate is the quotient of two quantities in different units of measurement, often represented as a fraction. If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change in the other (dependent) variable. One common type of rate is "per unit of time", such as speed, heart rate, and flux.
Product differentiationIn economics and marketing, product differentiation (or simply differentiation) is the process of distinguishing a product or service from others to make it more attractive to a particular target market. This involves differentiating it from competitors' products as well as from a firm's other products. The concept was proposed by Edward Chamberlin in his 1933 book, The Theory of Monopolistic Competition. Firms have different resource endowments that enable them to construct specific competitive advantages over competitors.
Chain ruleIn calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g. More precisely, if is the function such that for every x, then the chain rule is, in Lagrange's notation, or, equivalently, The chain rule may also be expressed in Leibniz's notation. If a variable z depends on the variable y, which itself depends on the variable x (that is, y and z are dependent variables), then z depends on x as well, via the intermediate variable y.
Psychoanalytic film theoryPsychoanalytic film theory is a school of academic thought that evokes the concepts of psychoanalysts Sigmund Freud and Jacques Lacan. The theory is closely tied to Critical theory, Marxist film theory, and Apparatus theory. The theory is separated into two waves. The first wave occurred in the 1960s and 70s. The second wave became popular in the 1980s and 90s. At the end of the nineteenth century, psychoanalysis was created, and film happened to follow shortly afterward.
Notation for differentiationIn differential calculus, there is no single uniform notation for differentiation. Instead, various notations for the derivative of a function or variable have been proposed by various mathematicians. The usefulness of each notation varies with the context, and it is sometimes advantageous to use more than one notation in a given context. The most common notations for differentiation (and its opposite operation, the antidifferentiation or indefinite integration) are listed below.
Area under the curve (pharmacokinetics)In the field of pharmacokinetics, the area under the curve (AUC) is the definite integral of the concentration of a drug in blood plasma as a function of time (this can be done using liquid chromatography–mass spectrometry). In practice, the drug concentration is measured at certain discrete points in time and the trapezoidal rule is used to estimate AUC. In pharmacology, the area under the plot of plasma concentration of a drug versus time after dosage (called “area under the curve” or AUC) gives insight into the extent of exposure to a drug and its clearance rate from the body.
Intraspecific competitionIntraspecific competition is an interaction in population ecology, whereby members of the same species compete for limited resources. This leads to a reduction in fitness for both individuals, but the more fit individual survives and is able to reproduce. By contrast, interspecific competition occurs when members of different species compete for a shared resource. Members of the same species have rather similar requirements for resources, whereas different species have a smaller contested resource overlap, resulting in intraspecific competition generally being a stronger force than interspecific competition.
Cmax (pharmacology)DISPLAYTITLE:Cmax (pharmacology) Cmax is the maximum (or peak) serum concentration that a drug achieves in a specified compartment or test area of the body after the drug has been administered and before the administration of a second dose. It is a standard measurement in pharmacokinetics. Cmax is the opposite of Cmin, which is the minimum (or trough) concentration that a drug achieves after dosing. The related pharmacokinetic parameter tmax is the time at which the Cmax is observed.
All models are wrongAll models are wrong is a common aphorism and anapodoton in statistics; it is often expanded as "All models are wrong, but some are useful". The aphorism acknowledges that statistical models always fall short of the complexities of reality but can still be useful nonetheless. The aphorism originally referred just to statistical models, but it is now sometimes used for scientific models in general. The aphorism is generally attributed to the statistician George Box. The underlying concept, though, predates Box's writings.
