Symbolic computation of gradient

[v0id]

I'm wondering if there are any convenient symbolic "shortcuts" (i.e. abuse of notation) that enable one to compute the gradient with respect to a certain vector, without decomposing the computation into the vector's individual elements and differentiating with respect to each element. For example:
<br /> \nabla_x \left( \frac{1}{|{\bf x}^{&#039;} - {\bf x}|} \right) = \frac{{\bf x}^{&#039;} - {\bf x}}{|{\bf x}^{&#039;} - {\bf x}|^3}<br />
Besides the obvious method of evaluating \frac{\partial}{\partial x_1} and so on, is there a faster method of symbolic computation?

 

[ansrivas]

If you consider
\sqrt{x^Tx}=|x|
then symbolic ideas help to get to the final expression:

\nabla_x \left( (x&#039;-x)^{T}(x&#039;-x) \right)^{-1/2} = \left( (x&#039;-x)^{T}(x&#039;-x) \right)^{-3/2} (x&#039;-x)

 

[v0id]

Yes, that works very well. Thanks a lot.