高等数学多元微分题设f(x,y,z)=xy^2+yz^2+zx^2,求fxx(0,0,1)fxz(1,0,2)及fzzx(2,0,1)怎么做？？

Question

高等数学多元微分题设f(x,y,z)=xy^2+yz^2+zx^2,求fxx(0,0,1) fxz(1,0,2) 及fzzx(2,0,1)怎么做？？

Answer 1

fx(x,y,z)=∂f/∂x=y²+yz²+2zx
fz(x,y,z)=∂f/∂z=2yz+z
fxx(x,y,z)=∂²f/∂x² = 2z
fxz(x,yz) = ∂²f/∂x∂z=2yz+2x
fzz(x,y,z) =∂²f/∂z²=2y+1
fzzx(x,y,z) =∂³f/∂z³=0
∴ fxx(0,0,1)=2
fxz(1,0,2) = 2
fzzx(2,0,1) = 0