CHAPTER VI.
SUMS, DIFFERENCES, PRODUCTS AND QUOTIENTS.
We have learned how to differentiate simple algebraical functions such as or , and we have now to consider how to tackle the sum of two or more functions.
For instance, let
;
what will its be? How are we to go to work on this new job?
The answer to this question is quite simple: just differentiate them, one after the other, thus:
. (Ans.)
If you have any doubt whether this is right, try a more general case, working it by first principles. And this is the way.
Let , where u is any function of , and any other function of . Then, letting increase to , will increase to ; and will increase to ; and to .