  Universal geometric calculus simplifies and unifies the structure and
notation of mathematics for all of science and engineering, and for
technological applications. This paper treats the fundamentals of the
multivector differential calculus part of geometric calculus. The multivector
differential is introduced, followed by the multivector derivative and the
adjoint of multivector functions. The basic rules of multivector
differentiation are derived explicitly, as well as a variety of basic
multivector derivatives. Finally factorization, which relates functions of
vector variables and multivector variables is discussed, and the concepts of
both simplicial variables and derivatives are explained. Everything is proven
explicitly in a very elementary level step by step approach. The paper is thus
intended to serve as reference material, providing a number of details, which
are usually skipped in more advanced discussions of the subject matter. The
arrangement of the material closely follows {chapter 2 of D. Hestenes, G.
Sobczyk, Clifford Algebra to Geometric Calculus, Kluwer, Dordrecht, 1999}.
