let f = u1.u2 = u11u21 + u12u22 = f(x,y)

delf = df/dxi+df/dyj

del acosf = [d(acosf)/dx]i+ [d(acosf) /dy]j= -1/sqrt(1-f^2)[(df/dx)i+(df/dy)j]

del acosf = -1/sqrt(1-f^2)delf

delf = u21delu11 + u21delu22 + u11delu21 + u12delu22, or

delf = delu1.u2 = u1.delu2 + u2.delu1 + u1x(delxu2) + u2x(delxu1) look it up, or google

Same in 3 dimensions just more to write. If u1 and u2 are orthogonal unit vectors, go back and think about it, oh well, then u1.u2 =1 and delf=0, so probably not.

Didn't feel like bolding del and all the vectors, ie, del =deland u1 =u1 etc. U11..are scalars, d is partial.