Let f(x,y,z)=2ln(x+y+z^(2)), with x+y+z>0.
Find gradf.
A. (2)/(x+y+z^(2))
B. (2)/(x+y+z^(2))([1],[1],[2z])
C. (2)/(x+y+z^(2))([1],[1],[1])
D. 2(x+y+z^(2))([1],[1],[2z])
Let f(x,y,z)=2ln(x+y+z^(2)), with x+y+z>0.
Find the directional derivative
(delf)/(delb)(x,y,z),
where b=(1,0,2) at the point (x,y,z)=(1,1,1).
A. (2sqrt(5))/(3)
B. (2)/(3sqrt(5))
C. (2)/(3)
D. (2+2z)/(sqrt(5))
0<z+X+xy7!M(zz+X+x)u1Z=(z'Xx)Jo7 o Find Vf.
1 2 1 X+y+z2 2z
2
A.
B.
x+y+ z2
/1 2 C. 1 x+y+z2 1
1 D.2(x+y+ z2) 1 2z
0< z+X+x y7!M(zz+X+x)u1Z=(zX x)y7o7 o Find the directional derivative
of
where b = (1,0,2) at the point (x,y,z) = (1,1,1) 2v5 A. 3 2 B. 3v5 2 C. 13 2+ 2z D. V5
