1=e^u*pu/px+cosv*pv/px （为书写方便，用"p“代表求偏导算符）
y=e＾u-cosv 两边对x求导，得
0=e^u*pu/px+sinv*pv/px
联立可解得
pu/px=sinv/[e^u*(sinv-cosv)]
...确定隐函数u=f(x,y)和v=g(x,y)的偏导数du\/dx...求过程
解：x=e＾u+sinv 两边对x求导，得 1=e^u*pu\/px+cosv*pv\/px （为书写方便，用"p“代表求偏导算符）y=e＾u-cosv 两边对x求导，得 0=e^u*pu\/px+sinv*pv\/px 联立可解得 pu\/px=sinv\/[e^u*(sinv-cosv)]
...x=e∧u+usinv,y=e∧u-ucosv;求u对x的偏导 和v对y的偏导.
x=e∧u+usinv,对x求偏导,得1=e^u*əu\/əx+əu\/əx*sinv+ucosv*əv\/əx………（1）y=e∧u-ucosv；对x求偏导,得0=e^u*əu\/əx-əu\/əx*cosv+usinv*əv\/əx,则əv\/əx=-(e^u-cosv)*(&...
设z=e^usinv 而u=xy v=x+y 求偏导数
=e^u sinv · x +e^u cosv · 1 =(xsinv+cosv) e^u 或 ^^^z=e^xy *(x+y)那么对x求偏导数得到 Z'x=(e^xy)' *(x+y)+e^xy *(x+y)'=y *e^xy *(x+y)+e^xy =e^xy *(xy+y^2+1)同理Z'y=e^xy *(xy+x^2+1)...
设z=e^usinv 而u=xy v=x+y 求偏导数
=e^u sinv · x +e^u cosv · 1 =(xsinv+cosv) e^u 解法二：1、对X的偏导数：u^z=e^xy *(x+y)，那么对x求偏导数得到 Z'x=(e^xy)' *(x+y)+e^xy *(x+y)'=y *e^xy *(x+y)+e^xy =e^xy *(xy+y^2+1)2、对Y的偏导数：Z'y=e^xy *(xy+x^2+1)...
设X=e^ucosv,Y=e^usinv,z=uv,求x关于z的偏导,和Y关于z的偏导。
由一阶微分形式不变性:dz=vdu+udv dX=e^u(cosvdu-sinvdv)dY=e^u(sinvdu+cosvdv)联立方程:du=(cosvdX+sinvdY)\/e^u,dv=(cosvdY-sinvdX)\/e^u,代入dz
设x=e^u乘cosv,y=e^u乘sinv,z=uv,求z对x偏导和z对y偏导
v = arctan(y\/x)z = uv = (1\/2)ln(x^2+y^2)arctan(y\/x)z'<x> = [x\/(x^2+y^2)]arctan(y\/x)+ (1\/2)ln(x^2+y^2)(-y\/x^2)\/[1+(y\/x)^2]= [x\/(x^2+y^2)]arctan(y\/x) - (1\/2)[y\/(x^2+y^2)]ln(x^2+y^2)z'<y> = [y\/(x^2+y^2...
x=e的U次方cosv,y=e的U次方sinv,z=Uv,求z对x偏导和z对y偏导
x=e的U次方cosv,y=e的U次方sinv,z=Uv,求z对x偏导和z对y偏导
Z=e∧u sinv,而u=xy,v=x+y,求az\/ax , az\/ay
z'(x)=e^u*ysinv+e^ucosv=e^(xy)(ysin(x+y)+cos(x+y))z'(y)=e^u*xsinv+e^ucosv=e^(xy)(xsin(x+y)+cos(x+y))
已知y=x+ux+sin v,u=e^x,v=ln x, 求dy\/dx 求解答。。谢谢了。。
dy\/dx=1+du\/dx*x+u*dx\/dx+cosv*dv\/dx =1+x*e^x+e^x+cos(lnx)*(1\/x)
设X=e∧u · cos v,Y=e∧u·sin v,z = uv .求аz\/аx,аz\/аy.
x=e^u*cosv,对x求导：1=e^ucosv* u'x-e^u sinv*v'x,得：cosv*u'x-sinv*v'x=1\/e^uy=e^u*sinv,对x求导：0=e^u sinv*u'x+e^ucosv*v'x,得：sinv*u'x+cosv*v'x=0解得：u'x=cosv\/e^u,v'x=-sinv\/e^uZ'x=Z'u* u'x+Z'v*v'x=v*...
