Broad intuition · Study map 7 of 85
Derivatives: a sensitivity meter
Suggested preparation: Vectors and matrices: coordinates that can move
Picture it
Turn one tiny knob and watch the output move. A derivative measures that local response. A gradient puts the sensitivities of all knobs into one vector. The chain rule connects sensitivities through a sequence of operations.
What to understand
- Partial derivatives and gradients
- Chain rule; add contributions when paths meet
Follow the references
1 · Video + article
3Blue1Brown · Visualizing the chain rule ↗Follow how a tiny input change passes through two composed functions; this is the picture behind multiplying derivatives.
2 · Video
3Blue1Brown · Backpropagation calculus ↗Focus on the chain-rule section; you can skip the longer algebra on a first pass.
You understand it when…
If a knob doubles an intermediate change and that intermediate triples the final change, what is the combined sensitivity?
This is a study map. Follow the reference for the full explanation; use the question to test your mental model. Browse the reference shelf.