Mathematical formulas

Differential Calculus

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Sections

  • 1Notation, functions and domains▸
  • 2Limits▸
  • 3Continuity▸
  • 4Derivative and geometric interpretation▸
  • 5Differentiation rules▸
  • 6Higher-order derivatives▸
  • 7Mean value theorem▸
  • 8Function analysis▸
  • 9Optimization▸
  • 10Linear approximations and differentials▸
  • 11Taylor series (introduction)▸
  • 12L'Hôpital and indeterminate limits▸
  • 13Implicit and related functions▸
  • 14Related rates▸
  • 15Graphs and asymptotic behavior▸
  • 16Guide to differentiate and analyze▸
  • AAppendix A: extended derivative table▸
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Featured topics

Limit algebra

Algebraic rules for combining limits: sum, product, quotient and the power [f(x)]^n.

Key formulas

  • DIF-015

    Valid if the limits of fff and ggg exist.

  • DIF-016
  • DIF-017
  • DIF-018
  • DIF-019

    Valid if the limit of fff exists. If n<0n<0n<0, also requires lim⁡x→af(x)≠0\lim_{x\to a}f(x)\neq0limx→a​f(x)=0.

Related sections

  • 2.4. Limit algebra

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