4. (i) Consider the function z = f (x,y) of two variable. The total differential of it (dz) is given by: dz = fx dx + fy dy. Prove that d²z = fxx dx² +2 fxy dx dy + fyy dy² fx = Əf/ Əx, fy = Əf/Əy, fxx = Ə²f/№x, £xy = Əf/ƏXƏy, £yy = Əf/2²y ] (ii) If z = x³ +5xy - y2 derive dz and the d²z

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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differential prove

4. (i) Consider the function z =f (x,y) of two variable. The total differential of it (dz)
is given by:
dz = fx dx + fy dy.
Prove that
d?z = fxx dx2 +2 fxy dx dy + fyy dy2
fx = əf/ əx , fy = Əf/ ây, fxx = Ə²f/ ²x , fxy = Pf/Əxây, fyy = a²f/²y |
%3D
%3D
(ii) If z = x3 +5xy - y2 derive dz and the d?z
Transcribed Image Text:4. (i) Consider the function z =f (x,y) of two variable. The total differential of it (dz) is given by: dz = fx dx + fy dy. Prove that d?z = fxx dx2 +2 fxy dx dy + fyy dy2 fx = əf/ əx , fy = Əf/ ây, fxx = Ə²f/ ²x , fxy = Pf/Əxây, fyy = a²f/²y | %3D %3D (ii) If z = x3 +5xy - y2 derive dz and the d?z
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