作业帮多元函数微分学 求下列函数的偏导数
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/06 01:56:33
多元函数微分学 求下列函数的偏导数
多元函数微分学 求下列函数的偏导数
多元函数微分学 求下列函数的偏导数
(1) u' = y+1/y, u' = x-x/y^2.
(2) u' = [1√(x^2+y^2)-x*x/√(x^2+y^2)]/(x^2+y^2)
= (x^2+y^2-x^2)/(x^2+y^2)^(3/2) = y^2/(x^2+y^2)^(3/2).
u' = -x*y/(x^2+y^2)^(3/2) = -xy/(x^2+y^2)^(3/2).
(3) u' = (1/y)/[1+(x/y)^2] = y/(x^2+y^2).
u' = (-x/y^2)/[1+(x/y)^2] = -x/(x^2+y^2).
(4) u' = sin(x+y)+xcos(x+y), u' = xcos(x+y).
(7) u = ln√(x^2+y^2) = (1/2)ln(x^2+y^2).
u' = (1/2)2x/(x^2+y^2) = x/(x^2+y^2),
u' = (1/2)2y/(x^2+y^2) = y/(x^2+y^2).