Usually you have identities for these kinds of things, but if you are trying to prove it then that's different?
Are you trying to simply calculate it or to prove what the result is?
Is this just a standard directional derivative with respect to some vector?
If so it's going to have some dot product and hence some matrix expansion in terms of b and the normal derivative of that matrix expression.
I can't recall the identities off the top of my head, but if you do a search they should be out there.
There are severals ways to find , because there are several ways to interpret it. I'll show you a kinda weird way, but one that's often very useful:
Think of a curve such that and .
Now, although there are infinitely many, is the natural choice for g. However, we won't even need that.
So , and since that holds for EVERY , have: