Question

设x+2y+z-2xyz^1/2=0求z对x,y的偏导数

Answer 1

简单计算一下即可，答案如图所示

Answer 2

2xy√Z = x+2y
4x²y²Z = (x+2y)²
8xy²Z+4x²y²Z'x = 2(x+2y) Z'x = [2(x+2y)-8xy²Z]/4x²y² (1)
8x²yZ+4x²y²Z'y = 4(x+2y) Z'y = [4(x+2y)-8xy²Z]/4x²y² (2)
还可以把Z的表达式代入(1)、(2)。