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Derivatives of Rational Functions

A term of the form

a1x + a0

where a1, a0 are real numbers, is called a linear term in x; if a1 ≠ 0, it is also called polynomial of degree one in x. A term of the form

a2 x2 + a1x + a0,   a2 ≠ 0

is called a polynomial of degree two in x, and, in general, a term of the form

anxn + an-1xn-1 + ... + a1x + a0, an ≠ 0

is called a polynomial of degree n in x.

A rational term in x is any term which is built up from the variable x and real numbers using the operations of addition, multiplication, subtraction, and division. For example every polynomial is a rational term and so are the terms

02_differentiation-88.gif

A linear function, polynomial function, or rational function is a function which is given by a linear term, polynomial, or rational term, respectively. In this section we shall establish a set of rules which enable us to quickly differentiate any rational function. The rules will also be useful later on in differentiating other functions.


Last Update: 2006-11-05