differentiation

differentiation, in biology, series of changes that occur in cells and tissues during development, resulting in their specialization. This, in turn, permits a greater variety of organisms. In plants, unspecialized cells, composing tissue called meristem, differentiate into vascular tissue (xylem and phloem; see wood), supportive tissue (sclerenchyma), and storage tissue (parenchyma). In animals, the tissues of the gastrula stage of the embryo differentiate into specialized tissues. While it is not fully understood what initiates this processs, it is known that each of the specialized cells in an organism carries a full set of genes, with all of the organism's genetic information, but each specialized cell expresses only part of it. That is, each cell only transcribes that DNA that it needs to do its specific tasks (see nucleic acid).

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differentiation

Mathematical process of finding the derivative of a function. Defined abstractly as a process involving limits, in practice it may be done using algebraic manipulations that rely on three basic formulas and four rules of operation. The formulas are: (1) the derivative of xⁿ is nx^{n − 1}, (2) the derivative of sin x is cos x, and (3) the derivative of the exponential function e^x is itself. The rules are: (1) (af + bg)′ = af′ + bg′, (2) (fg)′ = fg′ + gf′, (3) (f/g)′ = (gf′ − fg′)/g², and (4) (f(g))′ = f′(g)g′, where a and b are constants, f and g are functions, and a prime (′) indicates the derivative. The last formula is called the chain rule. The derivation and exploration of these formulas and rules is the subject of differential calculus. See also integration.