sin(x y)=e^xy的dy-搜答案-搜搜做题作业网

将y看成是关于x的函数即y=f(x)我们在求导的同时要记得y也要对x求导即dy/dx我们两边分别对x求导得e^x+e^y*dy/dx=cos(xy)*(y+x*dy/dx)移项e^x-y*cos(xy

方程两边对x求导,得：y+xy'+y'e^y=2y+2xy'y'e^y-xy'=y得y'=y/(e^y-x)因此dy=ydx/(e^y-x)

dy/dx=e^(xy)dy/e^y=e^xdx两边积分得-e^(-y)=e^x+C再问：你这样右边是e^(x+y)啊再答：噢令xy=p两边求导得y+xy'=p'y'=(p'-y)/x=(p'-p/x

e^(xy)+sin(xy)=y(y+xy')e^(xy)+(y+xy')cos(xy)=y'y'=(ye^(xy)+ycos(xy))/(1-xe^(xy)-xcos(xy))

满意请采纳,谢谢

先移项：e=e^y+xy,再两边对x求导：0=e^y*y'+y+x*y',解得：dy/dx=y'=-y/（e^y+x）

对方程取导数y+x(dy/dx)+(dy/dx)=0(dy/dx)(x+1)=-ydy/dx=(-y)/(x+1)

sin(x^2+y^2)+e^x-xy^2=0左右微分得到cos(x^2+y^2)*(2xdx+2ydy)+(e^x)dx-(y^2)dx-2xydy=0余下的求出dy就可以了

两端对x求导得y+xy'=e^(xy)*(y+xy')整理即可得dy/dx=y再问：y'=y+e^xy/e^xy-x?再答：是的啊，就是这样啦。

cos(x+y)(1+y')=y+xy'dy/dx=y'=[y-cos(x+y)]/[cos(x+y)-x]

两边同时求导..得：y-e^xy(yx')=0x'=y/(ye^xy)所以dy/dx=y/(ye^xy)

三种方法1式中同时对x求导-（y+xy‘）cosxy+2yy'=0解出y’2式中同时取微分d{sin(xy)+y^2-e^2}=dsin(xy)+dy^2-de^2=-cosxydxy+2ydy=-c

你好!两边对x求导：e^(xy)*(y+xy')-y^2=y'cosy解得y'=(y^2-ye^(xy))/(xe^(xy)-cosy)

两边分别求x的导数得：e^x+(y+xy')=0,即y'=-(e^x+y)/x,即：dy/dx=-(e^x+y)/x

y+xy'-cos(πy²)2πyy'=0y=[2πycos(πy²)-x]y'y'=y/[2πycos(πy²)-x]即：dy/dx=y/[2πycos(πy²

7=xy-e^(xy),求dy/dx

如图.

sin(xy)=x 求dx/dy

x/[sec(xy)-y]dx/dy.

dx/dy-3xy=xy^2dx/x=(y^2+3y)dy两边积分得：lnx=y^3/3+3y^2/2+c==>x=exp(y^3/3+3y^2/2+c)=Cexp(y^3/3+3y^2/2)C常数

答：xy=x-e^(xy)e^(xy)=x-xy=x(1-y)两边对x求导：(xy)'e^(xy)=1-y-xy'(y+xy')e^(xy)=1-y-xy'ye^(xy)+xy'e^(xy)+xy'=