e的x y次方-xy=1,求y的导数-搜答案-搜搜做题作业网

-xy（x的2次方y的5次方-xy的3次方-y）=-xy²(x²y的4次方-xy²-1)=-(xy²)[(xy²)²-(xy²)-

(太麻烦拉,给点分啊!)设v=x*x-y*y,u=exp{xy}那么dv/dx=2x(这里应该用偏导符号,代替一下),dv/dy=2y,du/dx=y*exp{xy},du/dy=x*exp{xy}那

原方程是xy=1-e^y?如果是的话将等式两边对X求导数得y+xy'=e^y*y'则y‘=y/(e^y-x)y'(0)=y/e^y

两边同时微分.e^ydy-ydx-xdy=0.变下形.答案就出来了

1.两边对x求导：2yy'-2y-2xy'=0y'=y/(y-x)2.两边对x求导：e^(xy)*(y+xy')+3y^2y'-5=0y'=[5-e^(xy)]/[xe^(xy)+3y^2]

该题为隐函数求导.xy+e^(xy)=1则y+xy'+e^(xy)(y+xy')=0解得：y'=-y/x解答完毕.

求二元函数全微分z=f[x²-y²,e^(xy)]设z=f(u,v),u=x²-y²,v=e^(xy)则dz=(∂f/∂u)du+(&#

z=arctan(x*e^x)z'={1/[1+(x*e^x)^2]}*(x*e^x)'(x*e^x)'=x'*e^x+x*(e^x)'=e^x+x*e^x=(x+1)*e^x所以dz/dx=(x+1

x^2+y^2+(xy)^2-4xy+1=0x^2-2xy+y^2+(xy)^2-2xy+1=0(x-y)^2+(xy-1)^2=0x-y=0,xy-1=0所以x-y=0,xy=1故(x-y)^200

xy=e^x-e^yd(xy)=d(e^x-e^y)xdy+ydx=e^xdx-e^ydy(x+e^y)dy=(e^x-y)dx则由dy/dx=(e^x-y)/(e^y+x)

(x^2-2xy+y^2)+(x^2+2x+1)=0(x-y)^2+(x+1)^2=0x=-1y=-1xy=1(xy)^2006=1

原式=3x的2次方y/（-1/2xy）-xy的2次方/（-1/2xy）+1/2xy/（-1/2xy）=-6x+2y-1

(xy)'=(e^（x+y）'y+xy'=e^(x+y)*(1+y')y'=[e^(x+y)-y]/[1-e^(x+y)]

求二元函数全微分z=f[x²-y²,e^(xy)]设z=f(u,v),u=x²-y²,v=e^(xy)则dz=(∂f/∂u)du+(&#

答：x的2次方-(3xy+4y的2次方）-（11xy-5y2的次方）-3x的2次方=x²++y²-14xy=7-14*（-1）=7+14=21

对x求导y+x*y'=e^(x+y)*(1+y')y+x*y'=e^(x+y)+e^(x+y)*y'所以dy/dx=[e^(x+y)-y]/[x-e^(x+y)]

原式=2x的2次方-y的2次方-3xy-x的2次方+2y的2次方-3xy=x的2次方+y的2次方-6xy=2-6×(-1/2)=2+3=5

xy=e^x-e^y两边求导得：y+xy'=e^x-y'*e^y解得：y'=(e^x-y)/(e^y+x)

解x²+y²=7xy=-15x²-(3xy+4y²)-(11xy-2y²)-7x²=(5x²-7x²)+(-3xy-11

min是指f(x)g(x)h(x)三个函数中的最小值