14.5 - 14.5: THE CHAIN RULE KIAM HEONG KWA We shall assume...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 14.5: THE CHAIN RULE KIAM HEONG KWA We shall assume all functions are differentiable in this section. 1. The Chain Rule Suppose that f is a function of the n variables x 1 , x 2 , , x n and each x i is a function of the m variables t 1 , t 2 , c , t m , then (1.1) f t j = n X i =1 f x i x i t j for each j , j = 1 , 2 , ,m . It should be noted that f/t j is evaluated at ( t 1 ,t 2 , ,t m ), f/x i is evaluated at the corresponding value of ( x 1 ,x 2 , ,x n ), i.e. at ( x 1 ( t 1 ,t 2 , ,t m ) ,x 2 ( t 1 ,t 2 , ,t m ) , ,x n ( t 1 ,t 2 , ,t m )) , and x i /t j is evaluated at ( t 1 ,t 2 , ,t m ). For instance, if f is a function of x , y , and z , while x , y , and z are functions of t , then df dt = f x dx dt + f y dy dt + f z dz dt . The functional dependence of these variables can be denoted by the tree diagram f x t y t z t As another instance, if f is a function of...
View Full Document

This note was uploaded on 11/11/2011 for the course MATH 254.01 taught by Professor Kwa during the Fall '10 term at Ohio State.

Page1 / 5

14.5 - 14.5: THE CHAIN RULE KIAM HEONG KWA We shall assume...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online