Question

If u = (-1/r)r, find the value of grad (div u) .

Answer 1

u=(-1/r)r

div u=div[(-1/r)r]=-2/r

grad (div u)=[grad (-2/r)= (2/r³) grad r]

grad f(r)=[f'(r) grad r]

[f'(r) grad r]= 2/r³(1/r)r= (2/r³)r