## Abstract

In the calculus of a function *f* of two real variables, i.e., of a two-dimensional vector variable (*x*,*y*), one usually works with the two partial derivatives ∂*f*/∂*x* and ∂*f*/∂*y* (to be formally defined in 3-4.1 below). The first of these is the limit of a certain quotient with numerator *f*(*x*+*t*,*y*)-*f*(*x*,*y*). In the terminology of vectors, this numerator may be written as *f*((*x*,*y*)+*t*(1,0))-*f*(*x*,*y*). If we now write simply *x* for (*x*,*y*) ∈ ℝ^{2} and simply *h* for (1,0) ∈ ℝ^{2}, then the numerator can be expressed quite compactly as *f*(*x*+*th*)-*f*(*x*). With this notation, it becomes clearer that the partial derivative.

## Keywords

Partial Derivative Open Subset Convex Subset Jacobian Matrix Interior Point
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## Copyright information

© Springer-Verlag London Limited 2011