Question

help me to solve the divergence of the vector v(div v)and its value at the point P if known:
v = (x^2, 4y^2, 9z^2)at the point P(-1,0,1/2)

Answer 1

The divergence of a vector field is:\[\nabla \cdot \vec{v}=\frac{\partial v_x}{\partial x}+\frac{\partial v_y}{\partial y}+\frac{\partial v_z}{\partial z}\]

Answer 2

[∇⋅v⃗ =\frac{∂(x^2)}{∂x}+\frac{∂(4y^2)}{∂y}+\frac{∂(9z^2)}{∂z}\]
right?

Answer 3

\[\frac{ d(x^2) }{ dx } + \frac{ d(4y^2) }{ dy } + \frac{ d(9z^2) }{ dz }\]

Answer 4

how about this @Xishem ???

Answer 5

Yep. That's fine. Continue.

Answer 6

2x + 8y + 18z, and the value at the point (-1,0,1/2) is 7
thankyou @Xishem, I understand now :)