Question

设Z=f(x,y)且f(x,x^2)=x^3+1,fx(x,x^2)=x^2-2x^3,则求fy(x,x^2)=?

Answer 1

f(x,x^2)=x^3+1,

Zx=3x^2

Zx=fx+2x *fy=x^2-2x^3+2xfy

fy=(Zx-x^2+2x^3)/2x

=(3x^2-x^2+2x^3)/2x=x/2+x^2