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DIFFERENTIAL CALCULUS.

CHAPTER I.

DIFFERENTIATION,

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 da' y being some function of X, and u some function of y. This theorem may be extended to any number of functions, so that

du du dv ds dy

do do do dy .... da Ex. (1) Let u = (a + bw*)". Then y= a + bx", u = y",

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Us

nmn-1

=

sin r 6

= COS

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du dx

11x + a

-a)

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