已知函数z=f(x^2+y^2,x^2-2y^2),且f具有二阶连续的偏导数,求a^2z/axay

Question

已知函数z=f(x^2+y^2,x^2-2y^2),且f具有二阶连续的偏导数,求a^2z/axay

Answer 1

z=f(x^2+y^2,x^2-2y^2),
∂z/∂x=2xf1+2xf2
∂²z/∂x∂y=2x(2yf11-4yf12+2yf21-4yf22)
=4xy(f11-f21-2f22)