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 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 + bar")".

Then y= a + bx", 4 = "",

dy

du nbach,

= my-) = m (a + bæ")"-'; dr

dy

du

therefore mnbon-'(a + bw*)-1.

da

du {x + (1 + x)}}

(2)

{x + (1 + )}},

da 2 (1 + 2*)

du (3)

nan-16 dc