设z=f(x,y),且f(x,x^2)=x^3+1,f'x(x,x^2)=x^2-2x^3,则f'y(x,x^2)=()A.0B.x^4-2x^6C.(x^2-2x^3)2D.x+x^2f'x(x,x^2)为对x偏导,f'y(x,x^2)为对y偏导

Question

设z=f(x,y),且f(x,x^2)=x^3+1,f'x(x,x^2)=x^2-2x^3,则f'y(x,x^2)=( )
A.0
B.x^4-2x^6
C.(x^2-2x^3)2
D.x+x^2
f'x(x,x^2) 为对x偏导,f'y(x,x^2)为对y偏导

Answer 1

选D.
dz=3(x^2)dx
dy=2xdx
dz=f'xdx+f'ydy
3(x^2)dx=(x^2-2x^3+2x*f'y)dx
f'y=x+x^2