When a function consists of products and quotients of roots and powers, it is generally most convenient to take the differential of the logarithm, or, as it is usually called, the logarithmic differential of the function.

(31) Let u= (a + x)" (b + x)",

If u =0 be an implicit function of two variables and

Functions of Two or more Variables.

(53) u = (-)

\x2 + y2

{y-x-2(xy)} yś dx + {x-y-2(xy)} x3 dy

2 (xy)3 (x + y)2*

dx

2x (x + y)2

du =

Cz

ax'

+ zdz.

a

(cz – ax)2 {(ay − bz) dx + (cz − ax) dy + (b x − cy) dz}.