Question

微积分某题

设函数f（x，y）具有二阶连续偏导数且满足方程(∂^2 f)/(∂x^2 )=(∂^2 f)/(∂y^2 )及条件f(x,2x)=x,
f^' x(x,2x)=x^2 ),则f^'' xx(x,2x)=......这道题怎么做

Answer 1

(∂^2 f)/(∂x^2 )=(∂^2 f)/(∂y^2 ),由于f^' x(x,2x)=(∂ f)/(∂x)+(∂ f)/(∂y)=x^2，那么两边对x求导可得f^'' xx(x,2x)=(∂^2 f)/(∂x^2 )+(∂^2 f)/(∂y^2)+2(∂^2 f)/(∂x∂y)=2x

追答

感觉这个题没太看懂，所以我可能没做对