Why do students mix up addition and multiplication, in the Multivariable Chain Rule with all partial derivatives?
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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?
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