Say I have two 3d vector functions A and B I would intuitively think that the xhat component of (A dot Nabla)B would be (dAx/dx+dAy/dy+dAz/dz)Bx but my book gives it as Ax*dBx/dx + Ay*dBx/dy + Az*dBx/dz why is this so? why isn't A dot nabla equal to (dAx/dx+dAy/dy+dAz/dz)? My book says that the dot product of 2 vectors is commutative, and it says hat although the del operator is not exactly a vector, we can treat it as such in most cases. It never mentions that taking dot products is NOT one of those cases, yet from this it seems that A dot nabla is NOT equal to nabla dot A I've been trying to prove the dot product rule for gradients for 2 hours and It is not working out cause I kept doing (A dot nabla)B and (B dot nabla)A the way I thought they should be done, which gives different results from how they are apparently supposed to be done, but the proper way contradicts what I thought I knew about the del operator so clearly I have some kind of misconception that I need straightened out. Thanks!