Question

求下列函数的偏导数

Answer 1

5）u = y/x + z/y - x/z .............(0)
∂u/∂x = -y/x² - 1/z...................(1)
∂u/∂y = 1/x -z/y².....................(2)
∂u/∂z = 1/y + x/z²....................(3)
..........................
6) u = x^(yz)..........................(*)
.....lnu = yz lnx.......................(**)
u'x/u = yz/x.............∂u/∂x = yzx^(yz)/x = yzx^(yz-1)..............(4)
u'y/u = zlnx.............∂u/∂y = zx^(yz) lnx...............................(5)
u'z/u = ylnx ............∂u/∂z = yx^(yz) lnx...............................(6)

Answer 2

要对 x 求导数，只需把 y, z 看成常数即可。