f(x, y) = (sin x)ln y
"f f
uxx - 2uxy - 6uyy = 0
¾ = x + 2y, · = 2x - y.
f(x, y) = ex ln(1 + y)
(0, 0)
1 1 1 1
f(x, y) = + + = 1
x y x2 y2

dl
"
Å‚ (0, 0) (1, 2)
Å‚
x2+y2+4

xdx+ydy
"
Å‚
Å‚
1+x2+y2
f(x, y) = ln(x + ln y)
"f f
uxx - 4uxy - 2uyy = 0
¾ = 3x + y, · = x - 3y.
f(x, y) = ey cos x
(0, 0)
1
f(x, y) = cos2 x + cos2 y x = y - Ä„
4

(y - x)dl Å‚ y = x3 (1, 1) (2, 8)
Å‚

"
x2dx + xydy Å‚
Å‚