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Differentiation

  • Satish Shirali
  • Harkrishan Lal Vasudeva
Chapter

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) ∈ ℝ2 and simply h for (1,0) ∈ ℝ2, 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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Indian Institute of Science Education and Research (Mohali)PanchkulaIndia
  2. 2.Indian Institute of Science Education and Research (Mohali)ChandigarhIndia

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