Derivatives

Start with the limit definition, then learn the algebraic rules and standard derivatives. The final note connects derivatives to critical points, monotonicity, extrema, and the shape of a function.

Keep the derivatives cheat sheet nearby for lookup; use the notes for meaning and derivation.

These notes cover real single-variable differentiation and elementary curve analysis, not a full numerical-analysis course. Review limits and continuity first.

1. Definitions: existence, difference quotients and local linear approximation.
2. Rules: how products and compositions transmit change.
3. Function table: formulas with domain conditions.
4. Critical points and applications: classify candidates, examine concavity and use tangent-based calculations.

Continue with partial derivatives and gradients when the output depends on several inputs.

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