partial derivative concept
| Definition | The rate of change of a function of a vector when one coordinate moves and the others stay fixed. The gradient collects them. Primer L, equation L.19. |
|---|---|
| Example | For f(x) = x1 squared + 3 x1 x2 the partial derivatives are 2 x1 + 3 x2 and 3 x1. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id partial-derivative, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation L.19. |
| Assumptions and scope | none |
| Prior art | none recorded |
| Evidence | none |
| Reviewed | semantic review 2026-09-09; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation L.19.
\[\nabla f(x)=\Big(\frac{\partial f}{\partial x_1},\dots,\frac{\partial f}{\partial x_d}\Big),\qquad f(x+\delta)\approx f(x)+\nabla f(x)\cdot\delta.\]
Conditions
none
Ledger
none
First stated
Primer L section L.9 of Data Mining as Observation, added in draft 0.3 (2026-09-09) for the ECE 514 readers whose first courses are far behind. The idea is standard and TSK Appendix A covers it at length.
Measurements
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Failures and corrections
none
Invariance envelope
none declared
Machine checked
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Used in
Data Mining as Observation primer L, chapters 0.
Related
See also
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Status
Generated 2026-09-10 by encyclopedia/generate.py; book
at observation-data-mining f3914f0; the commit of every record is listed
in the encyclopedia’s provenance.