SS(x y)*e^(x y)dxdy-搜答案-搜搜考试网

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

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

将xy-e^x+e^y=0两边取导得：ydx+xdy-e^xdx+e^ydy=0解得：dy/dx=﹙y--e^x﹚/﹙x-+e^y﹚当x=0时,∴e^y=1,y=0∴dy/dx|x=0=（0-1）/﹙

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)

y'e^y+e^x-y²-2xyy'=0y'=(e^x-y²)/(2xy-e^y)即：dy/dx=(e^x-y²)/(2xy-e^y)祝你开心!希望能帮到你,如果不懂,请

xy=e^(x+y),求dx/dy

ydx/dy+x=(e^x)(e^y)dx/dy+(e^x)(e^y)dx/dy=[(e^x)(e^y)-x]/[y-(e^x)(e^y)]dx/dy=(xy-x)/(y-xy)dx/dy=x(y-1

你说的没错,但是ydx是从d(xy)里面来的d(xy)有两项,xdy+ydx

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。

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

siny+e^x=xy^2,两边求微分,cosydy+e^xdx=d(xy^2)cosydy+e^xdx=y^2dx+2xydy整理,得(e^x-y^2)dx=(2xy-cosy)dydy/dx=(e

e∧x+y=xy,求dy/dx

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

7=xy-e^(xy),求dy/dx

如图.

对xy-e^x+e^y=0求微分得ydx+xdy-e^xdx+e^ydy=0(y-e^x)dx+(x+e^y)dy=0dy/dx=(x+e^y)/(e^x-y)

求dy/dx+y/x=e^(xy)

令e^(xy)=u,y=lnu/xDy/dx=[(x/u)*(du/dx)-lnu]/x²,∴(1/ux)*(du/dx)-lnu/x²+lnu/x²=u即du/u

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'=