求函数z=xy/√(x^2+y^2)当x=2,y=1,△x=0.01,△y=0.03时的全增量和全微分

Question

求函数z=xy/√(x^2+y^2) 当x=2,y=1,△x=0.01,△y=0.03时的全增量和全微分

Answer 1

x=2, y=1, z=2/√5
x=2.01, y=1.03, z=2.01*1.03/√(2.01^2+1.03^2)=0.916654385...
,△Z=0.916654385-2/√5=,0.02222
z'x= y^3/(x^2+y^2)^(3/2) x=2, y=1, z'x=1/5^(3/2)
z'y=x^3/(x^2+y^2)^(3/2) , x=2, y=1, z'y=8/5^(3/2)
dz=(dx+8dy)/5^(3/2)=(0.01+0.24)/5^(3/2)=(√5)/100=0.02236