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)

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)

xishem · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

how about this @Xishem ???

xishem · Answer

Yep. That's fine. Continue.

anonymous · Answer

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