n.
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 x n is n x 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) 2032; = a f 2032; + b g 2032; , (2) (fg) 2032; = f g 2032; + g f 2032; , (3) (f/g) 2032; = (gf 2032; -fg 2032; )/ g 2 , and (4) (f(g)) 2032; = f 2032; (g) g 2032; , where a and b are constants, f and g are functions, and a prime ( 2032; ) 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 .