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1. Let f, g : R" → R and let 9(t) = f(t, x2, ..., an) and (t) = g(t, x2, ., Tn) where x2, .., Tn are constant. (a) Give expressions for the derivatives ' and ' in terms of f and g. (b) From the single variable calculus result that for a,b ER we have (ay + by)' ag' + by', prove that fe dg +b Əx1 a(af + bg) = a. (c) From the single calculus result that (p)' = p'?b + pp', prove that a(fg) af dg = g + f- dx1

1. Let f, g : R" → R and let 9(t) = f(t, x2, ..., an) and (t) = g(t, x2, ., Tn) where x2, .., Tn are constant. (a) Give expressions for the derivatives ' and ' in terms of f and g. (b) From the single variable calculus result that for a,b ER we have (ay + by)' ag' + by', prove that fe dg +b Əx1 a(af + bg) = a. (c) From the single calculus result that (p)' = p'?b + pp', prove that a(fg) af dg = g + f- dx1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Let f, g : R" → R and let 9(t) = f(t, x2, ..., an) and (t) = g(t, x2, ., Tn) where x2, .., Tn are constant. (a) Give expressions for the derivatives ' and ' in terms of f and g. (b) From the single variable calculus result that for a,b ER we have (ay + by)' ag' + by', prove that fe dg +b Əx1 a(af + bg) = a. (c) From the single calculus result that (p)' = p'?b + pp', prove that a(fg) af dg = g + f- dx1
Transcribed Image Text:1. Let f, g : R" → R and let 9(t) = f(t, x2, ..., an) and (t) = g(t, x2, ., Tn) where x2, .., Tn are constant. (a) Give expressions for the derivatives ' and ' in terms of f and g. (b) From the single variable calculus result that for a,b ER we have (ay + by)' ag' + by', prove that fe dg +b Əx1 a(af + bg) = a. (c) From the single calculus result that (p)' = p'?b + pp', prove that a(fg) af dg = g + f- dx1
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