例1求z=x2+3x+y2在点(1,2)处的偏导数 解 0x=2x+3y; =3x+2y ay att1=2×1+3×2=8, y=2 =3×1+2×2=7 例2设乙=x"(x>0,x≠1) 求证x0z 1 az 十 2 y ax In x ay 证 vx x Inx ax例 1 求 2 2 z = x + 3xy + y 在点(1,2) 处的偏导数. 解 = x z 2x + 3 y ; = y z 3x + 2y . = = = 2 1 y x x z 21+ 32 = 8 , = = = 2 1 y x y z 31+ 22 = 7 . 例 2 设 y z = x (x 0, x 1), 求证 z y z x x z y x 2 ln 1 = + . 证 = x z , y−1 yx = y z x ln x, y