Now 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.
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. Notation We have seen the notation to denote the derivative of the function at the point . It is also convenient to use the notation to denote the same quantity. This is natural since it recalls the origin of the derivative as a rate of change.