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#3: Post edited by user avatar Sunny‭ · 2024-06-20T14:11:26Z (6 months ago)
  • Why do multivariate calculus students mix up addition and multiplication, in the Multivariable Chain Rule with all partial derivatives?
  • Why do students mix up addition and multiplication, in the Multivariable Chain Rule with all partial derivatives?
  • I have taught multivariate calculus for years. Annually, at least a student swaps + and ×. They trump up
  • >$\color{red}{\dfrac{\partial z}{\partial s} = (\dfrac{\partial z}{\partial x} + \dfrac{\partial x}{\partial s}) [\dfrac{\partial z}{\partial y} + \dfrac{\partial y}{\partial s}]}$
  • instead of this definition in James Stewart, Daniel Clegg, Saleem Watson. *Calculus Early Transcendentals* (2021 9 edn). Page 987.
  • ![](https://i.imgur.com/PChkqXN.jpeg)
  • This definition refers to “Theorem 1” scanned below.
  • ![](https://i.imgur.com/VB7XQbZ.jpeg)
  • #### Why ? What am I failing to teach? How can I teach this better? How can I forestall further Mix Ups?
  • I have taught multivariate calculus for years. Annually, some student always swaps + and ×. They trump up
  • >$\color{red}{\dfrac{\partial z}{\partial s} = (\dfrac{\partial z}{\partial x} + \dfrac{\partial x}{\partial s}) [\dfrac{\partial z}{\partial y} + \dfrac{\partial y}{\partial s}]}$
  • instead of this definition in James Stewart, Daniel Clegg, Saleem Watson. *Calculus Early Transcendentals* (2021 9 edn). Page 987.
  • ![](https://i.imgur.com/PChkqXN.jpeg)
  • This definition refers to “Theorem 1” scanned below.
  • ![](https://i.imgur.com/VB7XQbZ.jpeg)
  • #### Why ? What am I failing to teach? How can I teach this better? How can I forestall further Mix Ups?
#2: Post edited by user avatar Sunny‭ · 2024-06-20T12:33:00Z (6 months ago)
  • I have taught multivariate calculus for 9 years. Annually, at least a student swaps + and ×. They trump up
  • >$\color{red}{\dfrac{\partial z}{\partial s} = (\dfrac{\partial z}{\partial x} + \dfrac{\partial x}{\partial s}) [\dfrac{\partial z}{\partial y} + \dfrac{\partial y}{\partial s}]}$
  • instead of this definition in James Stewart, Daniel Clegg, Saleem Watson. *Calculus Early Transcendentals* (2021 9 edn). Page 987.
  • ![](https://imgur.com/PChkqXN)
  • This definition refers to “Theorem 1” scanned below.
  • ![](https://i.imgur.com/VB7XQbZ.jpeg)
  • #### Why ? What am I failing to teach? How can I teach this better? How can I forestall further Mix Ups?
  • I have taught multivariate calculus for years. Annually, at least a student swaps + and ×. They trump up
  • >$\color{red}{\dfrac{\partial z}{\partial s} = (\dfrac{\partial z}{\partial x} + \dfrac{\partial x}{\partial s}) [\dfrac{\partial z}{\partial y} + \dfrac{\partial y}{\partial s}]}$
  • instead of this definition in James Stewart, Daniel Clegg, Saleem Watson. *Calculus Early Transcendentals* (2021 9 edn). Page 987.
  • ![](https://i.imgur.com/PChkqXN.jpeg)
  • This definition refers to “Theorem 1” scanned below.
  • ![](https://i.imgur.com/VB7XQbZ.jpeg)
  • #### Why ? What am I failing to teach? How can I teach this better? How can I forestall further Mix Ups?
#1: Initial revision by user avatar Sunny‭ · 2024-06-20T12:28:44Z (6 months ago)
Why do multivariate calculus students mix up addition and multiplication, in the Multivariable Chain Rule with all partial derivatives?   
I have taught multivariate calculus for 9 years. Annually, at least a student swaps + and ×. They trump up

>$\color{red}{\dfrac{\partial z}{\partial s}  = (\dfrac{\partial z}{\partial x} + \dfrac{\partial x}{\partial s}) [\dfrac{\partial z}{\partial y} + \dfrac{\partial y}{\partial s}]}$

instead of this definition in James Stewart, Daniel Clegg, Saleem Watson. *Calculus Early Transcendentals* (2021 9 edn). Page 987.
  
![](https://imgur.com/PChkqXN)

This definition refers to “Theorem 1” scanned below. 

![](https://i.imgur.com/VB7XQbZ.jpeg)


#### Why ? What am I failing to teach? How can I teach this better? How can I forestall further Mix Ups?