Question

求下列隐函数的导数1）X^3-Y^3-X-Y+XY=2(2)xe^y-ye^x=x

Answer 1

1）X^3-Y^3-X-Y+XY=2

3x^2-3y^2*y'-1-y'+y+xy'=0

y'=(3x^2-1+y)/(3y^2+1-x)

(2)xe^y-ye^x=x

e^y+x*e^y*y'-[y'e^x+ye^x]=1

e^y+xe^y*y'-y'e^x-ye^x=1

y'=(1+ye^x-e^y)/(xe^y-e^x)