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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
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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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
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
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