Functions of One Variable.

If u be an explicit function of X, which is of a complicated form, it may generally be reduced to the differentiation of simpler functions by means of the theorem

du du dy

dx dy 'dx y being some function of x, and u some function of y. This theorem may be extended to any number of functions,

Ex. (1) Let U =

(a + 600*)". Then y= a + b2",

y",

dy

du

= nb.-!, = my-) = m (a + b2")");

dr

du

therefore = mnban-'(a + b.w*)"-1.

dc

du {x + (1 + x2)"}! (2) = {x + (1 + 0*)},

2 (1 + 0*)!

du

U = eth; = nxn-en

dc