第6章 6.8

(1)

$z = xy$

$dz = ydx + xdy$

(2)

$z = \log(x^2+y^2)$

$dz = \frac{2x}{x^2+y^2}dx + \frac{2y}{x^2+y^2}dy = \frac{2(xdx+ydy)}{x^2+y^2}$

(3)

$z = \frac{y}{x}$

$dz = -\frac{y}{x^2}dx + \frac{1}{x}dy$

(4)

$z = \sin^{-1}\frac{y}{x} \qquad (x>0)$

$dz = \frac{-\frac{y}{x}}{\sqrt{x^2+y^2}}dx + \frac{1}{\sqrt{x^2+y^2}}dy = \frac{xdy-ydx}{x\sqrt{x^2+y^2}}$