Post History
#3: Post edited
by
Sunny
·
2024-06-20T14:11:26Z (8 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.
- 
- This definition refers to “Theorem 1” scanned below.
- 
- #### 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.
- 
- This definition refers to “Theorem 1” scanned below.
- 
- #### Why ? What am I failing to teach? How can I teach this better? How can I forestall further Mix Ups?
#2: Post edited
by
Sunny
·
2024-06-20T12:33:00Z (8 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.
- This definition refers to “Theorem 1” scanned below.
- 
- #### 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.
- 
- This definition refers to “Theorem 1” scanned below.
- 
- #### Why ? What am I failing to teach? How can I teach this better? How can I forestall further Mix Ups?
#1: Initial revision
by
Sunny
·
2024-06-20T12:28:44Z (8 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.
This definition refers to “Theorem 1” scanned below.
#### Why ? What am I failing to teach? How can I teach this better? How can I forestall further Mix Ups?