Question

已知f(u,v)可微,f(x,x^2)=x^3,fu(x,x^2)=x^2-x^4,求fv(x,x^2)

Answer 1

df(x,x^2)=fu·dx+fv·d(x^2)

∴ 3·x^2dx=(x^2-x^4)·dx+fv·2xdx

∴ fv·2x=2x^2+x^4

∴fv=x+(x^3)/2