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CHAPTER V.
NEXT STAGE. WHAT TO DO WITH CONSTANTS.

In our equations we have regarded as growing, and as a result of being made to grow also changed its value and grew. We usually think of as a quantity that we can vary; and, regarding the variation of as a sort of cause, we consider the resulting variation of as an effect. In other words, we regard the value of as depending on that of . Both and are variables, but is the one that we operate upon, and is the “dependent variable.” In all the preceding chapter we have been trying to find out rules for the proportion which the dependent variation in bears to the variation independently made in .

Our next step is to find out what effect on the process of differentiating is caused by the presence of constants, that is, of numbers which don’t change when or change their values.

Added Constants.

Let us begin with some simple case of an added constant, thus:

Let

.

Just as before, let us suppose to grow to and to grow to .