FUNCTIONS OF N VARIABLES Josefa Ramoni- Giampaolo Orlandoni
PARTIAL DERIVATIVES Continuity is still a condition for differentiability: f(x), x Rn is at a point x=a if it has no jumps or breaks as x approaches a. For functions of one variable, there are only two possible directions from which x approaches a: right and left. Limxa- f(x) = Limxa+ f(x) = f(a) For functions of more than on variable there exist an infinite number of directions from which a point in Rn can be approached A function f(x), x Rn, is continuous at a point x=a if, in the neighborhood around x=a, the Euclidean distance between f(x) and f(a) tends to zero as x tends to a x-a = (x1,x2)-(a1,a2) = ((x1-a1)2+(x2-a2)2) for R2

The rules of differentiation can …ver más…

Las

dX dY dZ son derivadas , , dR dR dR

ordinarias (X,Y,Z son función sólo de R)

Z = f(X,Y) Y = g(X)

f dY dZ f   dX X Y dX

dZ es una DERIVADA TOTAL y se dX compone de dos partes: 1. Efecto Directo de X en Z 2. Efecto Indirecto de X en Z a través de Y

Bibliography Hess, Peter (2002). Using Mathematics in Economics Analysis. Prentice