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Mathematics

Using the Chain Rule in Multivariable Calculus

Quick fact

The multivariable chain rule is the engine behind backpropagation in neural networks, allowing millions of parameters to be updated in a single training step.

Why this is interesting

You know how to differentiate a function of one variable — but what happens when a change in one variable triggers a cascade of changes through many others? How do you find the total rate of change when everything is connected?