x^y-e^2y=siny

xy-eˆ(2x)=siny两边对x求导,得y+x(dy/dx)-2eˆ(2x)=(cosy)*(dy/dx)(x-cosy)*(dy/dx)=2eˆ(2x)-ydy/d

利用格林公式设P=e^xsiny-2yQ=e^xcosy-z(这儿不可能是z,是x还是2呢,先作为2来解)Q对x求偏导数=e^xcosy,P对y求偏导数=e^xcosy-2差为2不等于0连接半圆的直径

[sin(2x+y)/sinx]-2cos(x+y)={[sin(x+y)cosx+cos(x+y)sinx]/sinx}-2cos(x+y)={[sin(x+y)cosx+cos(x+y)sinx-

再问：大哥，你题目看错了。。。再答：哪里有错？再问：第一条等式就错了。。是sin(x+y)=sinx+siny。后面是cos（x+y）·（1+y'）=cosx+cosy·y'？再答：OK，那我改下

sin(x+y)sin(x-y)=-1/2(cos(x+y+x-y)—cos(x+y-x+y))=-1/2(cos2x—cos2y)=-1/2(1-2（sinx）^2-1+2(siny）^2)=（si

sin(x+y)sin(x-y)=-1/2(cos(x+y+x-y)—cos(x+y-x+y))=-1/2(cos2x—cos2y)=-1/2(1-2（sinx）^2-1+2(siny）^2)=（si

这是隐函数啊,利用隐函数求导法则方程两边同时关于X求导,注意y是x的函数,即得如下:2xy+x^2y'-2e^(2y)y'=cosyy'整理一下(x^2-2e^(2y)-cosy)y'=-2xyy'=

设A=(X+Y)/2,B=(X-Y)/2X=A+B,Y=A-BSINX=SIN(A+B)=SINACOSB+COSASINBSINY=SIN(A-B)=SINACOSB-COSASINBSINX+SI

用隐函数求导一般得出的还是隐函数用WPS纯手打的,如果我理解错了你的式子,请指出,我改一下就行了,但方法是一样的再问：对不起没看到你的答案

∫e^ysinydy=-∫e^yd(cosy)=-[e^y*cosy-∫cosyd(e^y)]=∫cosy*e^ydy-e^ycosy=∫e^yd(siny)-e^ycosy=e^ysiny-∫sin

应该是2x^(2y)y'-2e^(2X)-cos(y)y'=0再问：2x^(2y)y'里2y的项是怎么来的呢？再答：好像求错了，是x^(2y-1)+2x^(2y)ln(x)y'-2e^(2X)-cos

令a=x+y,则条件变为3sin(a-x)=sin(a+x),展开得3sinacosx-3cosasinx=sinacosx+cosasinx,移项2sinacosx=4cosasinxtana=2t

x*e^y+siny=0e^y+x*e^y*y'+cosy*y'=0=>y'=-e^y/[xe^y+cosy]再问：你好！我数学太烂。。能不能补充一下完整的答案。。。再答：x*e^y+siny=0两边

sin[(x+y)+x]=5sin[(x+y)-x]sin(x+y)·cosx＋cos(x+y)·sinx＝5·sin(x+y)·cosx－5·cos(x+y)·sinx4·sin(x+y)·cosx

sinx+siny=sin[(x+y)/2+(x-y)/2]+sin[(x+y)/2-(x-y)/2]=sin(x+y)/2*cos(x-y)/2+cos(x+y)/2*sin(x-y)/2+sin(

|2sin[(x-y)/2]cos[(x+y)/2]|=I2[sin(x/2)cos(y/2)-sin(y/2)cos(x/2)][cos(x/2)cos(y/2)-sin(x/2)(sin(y/2)

把5siny=sin(2x+y)变为5sin[(x+y)-x]=sin[（x+y)+x],把其中的（x+y）,看成一个整体,上式即变为4sin(x+y)cosx=6cos(x+y)sinx,再把式子的

这是隐函数的求导cosy*y'+3e^3x-6x^2y^2-4x^3*y*y'=0dy/dx=y'=(6x^2y^2-3e^3x)/(cosy-4x^3y)

x+y=x+y/2+y/2x=x+y/2-y/2sin(x+y)=sin(x+y/2+y/2)=sin(x+y/2)cosy/2+cos(x+y/2)siny/2sinx=sin(x+y/2)cosy

两边对x求导有1-y'+y'cosy=0所以y'=1/(cosy-1)