# Introduction

Thus far we have represented the derivative of by the notation

We have taken special pains to impress on the student that the symbol

was to be considered not as an ordinary fraction with as numerator and as denominator, but as a single symbol denoting the limit of the quotient

as approaches the limit zero.

Problems do occur, however, where it is very convenient to be able to give a meaning to and separately, and it is especially useful in applications of the Integral Calculus. How this may be done is explained in what follows.

david joyner 2008-11-22