Proving the chain rule

Zhibin Yan

doi:10.1080/0020739X.2025.2530963

Proving the chain rule

Zhibin Yan^*

^*Corresponding author for this work

Harbin Institute of Technology Shenzhen

Research output: Contribution to journal › Comment/debate

Abstract

One common proof of the chain rule constructs an auxiliary function and causes some difficulty for learning and teaching. Another common proof based on the notion of the differential fails in its existing form. A new proof is given, which directly faces the subtle point that dependent variable and independent variable have different behaviours in the definition of the limit of a function.

Original language	English
Journal	International Journal of Mathematical Education in Science and Technology
DOIs	https://doi.org/10.1080/0020739X.2025.2530963
State	Accepted/In press - 2025
Externally published	Yes

Keywords

Limit
derivative
differential
the chain rule

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10.1080/0020739X.2025.2530963

Cite this

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abstract = "One common proof of the chain rule constructs an auxiliary function and causes some difficulty for learning and teaching. Another common proof based on the notion of the differential fails in its existing form. A new proof is given, which directly faces the subtle point that dependent variable and independent variable have different behaviours in the definition of the limit of a function.",

keywords = "Limit, derivative, differential, the chain rule",

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AB - One common proof of the chain rule constructs an auxiliary function and causes some difficulty for learning and teaching. Another common proof based on the notion of the differential fails in its existing form. A new proof is given, which directly faces the subtle point that dependent variable and independent variable have different behaviours in the definition of the limit of a function.

KW - Limit

KW - derivative

KW - differential

KW - the chain rule

UR - https://www.scopus.com/pages/publications/105013581557

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DO - 10.1080/0020739X.2025.2530963

M3 - 评论/辩论

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SN - 0020-739X

JO - International Journal of Mathematical Education in Science and Technology

JF - International Journal of Mathematical Education in Science and Technology

ER -

Proving the chain rule

Abstract

Keywords

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