dz dz Draw a dependency diagram and write a chain rule formula for and dn др z=g(x,y), x = f(n,p), y =h(n,p) Choose the correct dependency diagram for əz/an. B. 7 ?x ду Ən dn B X дz дz дх ду n О А. X dz ду ду ди Z n дz ?х dx on y 一 y - given the functions below. 0 с. X dn дх дх дz n 7 ди ду ду дz X D. дz дх дх dn Z n дz ду у ду dn
dz dz Draw a dependency diagram and write a chain rule formula for and dn др z=g(x,y), x = f(n,p), y =h(n,p) Choose the correct dependency diagram for əz/an. B. 7 ?x ду Ən dn B X дz дz дх ду n О А. X dz ду ду ди Z n дz ?х dx on y 一 y - given the functions below. 0 с. X dn дх дх дz n 7 ди ду ду дz X D. дz дх дх dn Z n дz ду у ду dn
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
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![The image features a problem asking to draw a dependency diagram and write a chain rule formula for the partial derivatives \(\frac{\partial z}{\partial n}\) and \(\frac{\partial z}{\partial p}\) given functions defined as \(z = g(x,y)\), \(x = f(n,p)\), and \(y = h(n,p)\).
Below this, it asks to choose the correct dependency diagram for \(\frac{\partial z}{\partial n}\) from the options given:
**Option A:**
- Shape: Diamond
- At the top, \(z\).
- On the left, \(\frac{\partial z}{\partial y}\) and \(\frac{\partial y}{\partial n}\).
- On the right, \(\frac{\partial z}{\partial x}\) and \(\frac{\partial x}{\partial n}\).
- At the bottom, \(n\).
**Option B:**
- Shape: Diamond
- At the top, \(z\).
- On the left, \(\frac{\partial x}{\partial n}\).
- On the right, \(\frac{\partial y}{\partial n}\).
- At the bottom, \(n\).
- \(\frac{\partial z}{\partial x}\) between \(x\) and \(z\).
- \(\frac{\partial z}{\partial y}\) between \(y\) and \(z\).
**Option C:**
- Shape: Diamond
- At the top, \(n\).
- To the right, \(\frac{\partial n}{\partial y}\) and \(\frac{\partial y}{\partial z}\).
- To the left, \(\frac{\partial n}{\partial x}\) and \(\frac{\partial x}{\partial z}\).
- At the bottom, \(z\).
**Option D:**
- Shape: Diamond
- At the top, \(z\).
- On the left, \(\frac{\partial z}{\partial x}\) and \(\frac{\partial x}{\partial n}\).
- On the right, \(\frac{\partial z}{\partial y}\) and \(\frac{\partial y}{\partial n}\).
- At the bottom, \(n\).
The task is to select the correct dependency diagram that represents the relationship for \(\frac{\partial z}{\partial](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb159ea24-ec33-411b-93d6-19afb03ffa76%2F1e1ae7a9-5221-44bb-b84e-cbe43a72a02a%2F88jjcfi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image features a problem asking to draw a dependency diagram and write a chain rule formula for the partial derivatives \(\frac{\partial z}{\partial n}\) and \(\frac{\partial z}{\partial p}\) given functions defined as \(z = g(x,y)\), \(x = f(n,p)\), and \(y = h(n,p)\).
Below this, it asks to choose the correct dependency diagram for \(\frac{\partial z}{\partial n}\) from the options given:
**Option A:**
- Shape: Diamond
- At the top, \(z\).
- On the left, \(\frac{\partial z}{\partial y}\) and \(\frac{\partial y}{\partial n}\).
- On the right, \(\frac{\partial z}{\partial x}\) and \(\frac{\partial x}{\partial n}\).
- At the bottom, \(n\).
**Option B:**
- Shape: Diamond
- At the top, \(z\).
- On the left, \(\frac{\partial x}{\partial n}\).
- On the right, \(\frac{\partial y}{\partial n}\).
- At the bottom, \(n\).
- \(\frac{\partial z}{\partial x}\) between \(x\) and \(z\).
- \(\frac{\partial z}{\partial y}\) between \(y\) and \(z\).
**Option C:**
- Shape: Diamond
- At the top, \(n\).
- To the right, \(\frac{\partial n}{\partial y}\) and \(\frac{\partial y}{\partial z}\).
- To the left, \(\frac{\partial n}{\partial x}\) and \(\frac{\partial x}{\partial z}\).
- At the bottom, \(z\).
**Option D:**
- Shape: Diamond
- At the top, \(z\).
- On the left, \(\frac{\partial z}{\partial x}\) and \(\frac{\partial x}{\partial n}\).
- On the right, \(\frac{\partial z}{\partial y}\) and \(\frac{\partial y}{\partial n}\).
- At the bottom, \(n\).
The task is to select the correct dependency diagram that represents the relationship for \(\frac{\partial z}{\partial
Expert Solution
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Step 1: Chain rule
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