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?