  This article shows a very elementary and straightforward proof of the
Implicit Function Theorem for differentiable maps $F(x,y)$ defined on a
finite-dimensional Euclidean space. There are no hypothesis on the continuity
of the partial derivatives of $F$. The proof employs determinants theory, the
mean-value theorem, the intermediate-value theorem, and Darboux's property (the
intermediate-value property for derivatives). The proof avoids compactness
arguments, fixed-point theorems, and integration theory. A stronger than the
classical version of the Inverse Function Theorem is also shown. An example is
given.
