Let $f ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$ , find $\nabla \cdot ( \nabla f )$ at the point $( 1,0,1 )$ .
A) $2$
B)
$4$
C)
$6$
D) $1$
E) $- 2$
F) $- 4$

G)
$- 6$
H)
$0$

Question

Let $f ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$ , find $\nabla \cdot ( \nabla f )$ at the point $( 1,0,1 )$ .
A) $2$ 
B)
$4$ 
C)
$6$
D) $1$
E) $- 2$
F) $- 4$

G)
$- 6$ 
H)
$0$

Quizplus · Accepted Answer

The gradient of $f$, $\nabla f$, is the vector of partial derivatives, $(2x, 2y, 2z)$. The divergence of $\nabla f$, $\nabla \cdot (\nabla f)$, is the sum of the second partial derivatives, $2 + 2 + 2 = 6$.

Let f(x,y,z)=x2+y2+z2f ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 }f(x,y,z)=x2+y2+z2

Let $f ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$