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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 nxn 1, (2) the derivative of sin x is cos x, and (3) the derivative of the exponential function ex is itself. The rules are: (1) (af + bg) = af + bg, (2) (fg) = fg + gf, (3) (f/g) = (gffg)/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 alsointegration.
This entry comes from Encyclopædia Britannica Concise. For the full entry on differentiation, visit Britannica.com.