Practice question · Multiple choice
The chain rule is the rule that makes almost every other derivative usable in practice. What is it actually saying about composed change?
Hints
- Gears: one turns three times per turn of the next, which turns twice per turn of the crank.
- Ask what dy/du × du/dx looks like if you treat the du symbols as cancelling.
Show the answer
C. That rates multiply through a chain: three times two is six
Why
Rates compose by multiplying, which the gear train makes obvious and the notation dy/du · du/dx makes memorable. It is also why backpropagation works: a neural network is a long composition, and the sensitivity of the loss to an early weight is a product of local derivatives along the chain.
Practise Differentiation Rules
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