Find the divergence of the vector field $\mathbf { F }$.
$$\mathbf { F } ( x , y , x ) = x z ^ { 2 } \mathbf { i } + 4 x ^ { 3 } z \mathbf { j } - 6 y ^ { 4 } z \mathbf { k }$$
Select the correct answer.
A) $z ^ { 2 } - 6 y ^ { 4 }$
B) $z ^ { 2 } \mathrm { i } + 4 x ^ { 3 } z \mathrm { j } - 6 y ^ { 4 } \mathrm { k }$
C) $z ^ { 2 } + 4 x ^ { 3 } z - 6 y ^ { 4 }$
D) $z ^ { 2 } \mathbf { i } - 6 y ^ { 4 } \mathbf { k }$

Question

Quizplus · Accepted Answer

The divergence of a vector field is given by the sum of the partial derivatives of its components. So, for the given vector field, we have:$$	ext{div} \mathbf{F} = \frac{\partial}{\partial x}(xz^2) + \frac{\partial}{\partial y}(4x^3z) + \frac{\partial}{\partial z}(-6y^4z) = z^2 - 6y^4$$

Find the Divergence of the Vector Field F\mathbf { F }F

Find the Divergence of the Vector Field $\mathbf { F }$