  We develop principal branches for three key square root functions and for the
inverse trigonometric and inverse hyperbolic functions. The three square root
branches are integral to defining the inverse function branches, their
derivatives, and their antiderivatives. Complex analysis is used to turn the
definitions of the principal branches into concrete expressions. We take the
standard reference in this area to be the NIST Digital Library of Mathematical
Functions (DLMF). We adopt the notation for, and the definitions of, the
principal branches of the inverse functions in the DLMF. Our goal is to widen
the scope of the results in the DLMF while at the same time lowering the
complex variables burden on the average DLMF user.
