CHAPTER VII.
SUCCESSIVE DIFFERENTIATION.
Let us try the effect of repeating several times over the operation of differentiating a function (see p. 14). Begin with a concrete case.
Let .
First differentiation, | . | |
Second differentiation, | . | |
Third differentiation, | . | |
Fourth differentiation, | . | |
Fifth differentiation, | . | |
Sixth differentiation, | . |
There is a certain notation, with which we are already acquainted (see p. 15), used by some writers, that is very convenient. This is to employ the general symbol for any function of . Here the symbol is read as “function of,” without saying what particular function is meant. So the statement merely tells us that is a function of , it may be or , or or any other complicated function of .
The corresponding symbol for the differential coefficient is , which is simpler to write than . This is called the “derived function” of .
C.M.E.
D