| UBC Calculus Online Course Notes |
Introduction to DerivativesNow that we have seen several ways of thinking about the derivative and have actually performed one calculation, we would like to develop some handy techniques to compute derivatives. In a way, this is like learning the multiplication tables after you understand what multiplication means. In this unit, we will learn how to compute the derivatives of rational functions. You may remember that polynomials are functions which are built in the simplest way possible---namely, through addition and multiplication. Rational functions are simply functions obtained by taking the quotient of two polynomials. For example, is a rational function. Later, we will learn how to differentiate more complicated expressions.
Before we get started though, we need to consider an important application of the derivative in approximating functions. |