The chain rule for differentiation is proved from first principles. Use is made of the small difference formula, which is discussed first.

The chain rule from 1st principles (MathsCasts)

These MathsCasts were produced by the mathematics support centres at Swinburne University, the University of Limerick and Loughborough University. They were part of a collaborative research project to develop high quality resources and investigate the effectiveness of MathsCasts to support mathematics learning. The full set of resources are available at http://commons.swin.edu.au/s/mathscasts MathsCasts are licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License

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The chain rule from 1st principles (MathsCasts)

The chain rule from 1st principles (MathsCasts)