Question

微积分，请问1.2.3.题怎么做，求详解

Answer 1

Answer 2

1)siny+e^x-xy^2=0
cosydy/dx+e^x-(y^2+x*2ydy/dx)=0
dy/dx=(y^2-e^x)/(cosy-2xy)
2)y=2xarctan(y/x)
dy/dx=2arctan(y/x)+2x*(arctan(y/x)')*(y/x)'
=2arctan(y/x)+2x*[1/(y^2/x^2+1)^0.5]*(dy/dx*x-y)/x^2
移项整理得
dy/dx=[2arctan(y/x)-y/(x^2+y^2)^0.5]/(1-2x/(x^2+y^2)^0.5)
3)x^2+y^2-z^2-xy=0
对x求偏导数
2x-2zdz/dx-y=0
dz/dx=(y-2x)/(-2z)
对y求偏导数
2y-2zdz/dy-x=0
dz/dy=(x-2y)/(-2z)