求解导数xy-xe^y^2-x=-2设xy-xe^y^2-x=-2,则当x=1,y=0时,dx/dy=?注；e^y^2是e的（y平方）次方

Question

求解导数xy-xe^y^2-x=-2
设xy-xe^y^2-x=-2,则当x=1,y=0时,dx/dy=?
注；e^y^2是e的（y平方）次方

Answer 1

∵xy-xe^(y²)-x=-2
==>xy'+y-e^(y²)-2xye^(y²)y'-1=0
==>x[1-2ye^(y²)]y'=e^(y²)-y+1
∴y'=[e^(y²)-y+1]/[x(1-2ye^(y²))]
故当x=1,y=0时,dx/dy=(1-0+1)/(1-0)=2.