divergence of a vector field

andrey21

Im just curious how you find the divergence of the following vector field





Heres my example

u = xz^(2)i +y(x^(2)-1)j+zx^(2) y^(3)k



Am I right in thinking

U take the derivative with respect to x for first term derivative with respect to y for second term......

giving me z^(2) + (x^(2) -1) +x^(2)y^(3)

LCKurtz

You have it correct.

andrey21

Thanks LCKurtz just another question I have bin posed.

does div(uxv)

Mean find the divergence of the dot product of vectors u and v.

LCKurtz

No. That wouldn't make any sense because a dot product gives a scalar and divergence applies to vector fields. What it does mean is first take the cross product of a and b, which gives a vector, then take its divergence.