Chain Rule Choices (az/Ən) Image attatched 1* Dependancy Diagrams for ðz/ðn. dz dz dy dz dx --+-- an dx dn dy dn dz dz dy dz and an dz 2 ay dy 4 dz dz dz dx dy 2 -=-- + on dx dy dn dn dy 3 dz dz dz dy + de an dy an 4 4 dz z dz d dz dy dn dx dn dy dn Dependancy Diagram options for az/əp. Chain Rule Choices (@z/Ənp) 1 2 3 4 dz dx dz dy =-+- +-+- op 1 1 dz dy 2 dz dz dz dx dy др dp дх ду др др dz dy P 3 dz dz dy dz dx %3D dp dx ap dy dp dz 4 xP zp dz dy dp dx dp dy dp -

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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Question

Draw a dependency diagram and write a chain rule formula for (image attatched 1*) given the functions below.

z = f(x,y), x = g(n,p), y = k(n,p)

i have attatched a big image, 

I need to choose the correct one for each of them if possible

thank you for your time

Chain Rule Choices (az/an) Image attatched 1*
Dependancy Diagrams for ðz/dn.
dz dz dy dz dx
1
an
n
+
on
dz
dz
dy
dx dn
ду дп
on
dx
dz
and
dp
dx
dy
2
ду
dx
3
dx
dy
4
dn
dz
dz dz dx dy
1
2
+ -
an
дх ду
an an
an
3 dz dz
z dx
dz dy
dx
dy
dy
dz
dz
dz
dn
dn
dx
an
dx
dn
dy an
n
n
n
dz
4
dz dx
dz dy
an
up xp
dy dn
Dependancy Diagram
options for az/dp.
Chain Rule Choices (ðz/ðnp)
dz
dz
dy
dz
2
3
4
дх
dx
dy
dx
1 dz dz dx dz
ду
+ -
+ - -
др дх др ду
dp' dy
dp
X-
dz
2
dz dz
dx dy
dy
dz
dx
др дх ду др др
dz
dz
dx
dy
др
dz dz dy
dz dx
3
др дх др
+
ду др
dz
4
др
dp
dz dx
dz dy
дх др ду др
Transcribed Image Text:Chain Rule Choices (az/an) Image attatched 1* Dependancy Diagrams for ðz/dn. dz dz dy dz dx 1 an n + on dz dz dy dx dn ду дп on dx dz and dp dx dy 2 ду dx 3 dx dy 4 dn dz dz dz dx dy 1 2 + - an дх ду an an an 3 dz dz z dx dz dy dx dy dy dz dz dz dn dn dx an dx dn dy an n n n dz 4 dz dx dz dy an up xp dy dn Dependancy Diagram options for az/dp. Chain Rule Choices (ðz/ðnp) dz dz dy dz 2 3 4 дх dx dy dx 1 dz dz dx dz ду + - + - - др дх др ду dp' dy dp X- dz 2 dz dz dx dy dy dz dx др дх ду др др dz dz dx dy др dz dz dy dz dx 3 др дх др + ду др dz 4 др dp dz dx dz dy дх др ду др
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