Question

设由方程xy+yz+xz=1,确定函数z=f(x,y),求∂2z／∂（x^2）

Answer 1

y+y∂z/∂x+z+x∂z/∂x=0

∂z/∂x=-(y+z)/(x+y)

∂2z/∂x2=【∂(∂z/∂x）】／∂x=【∂( -(y+z)/(x+y)）】／∂x=[-∂z/∂x(x+y)+(y+z)]/(x+y)^2 =2(y+z)/(x+y)^2