Everything About ___
Live briefing

Everything about Differentiable function

Mathematical function whose derivative exists

In mathematical analysis, a real or complex function of a single variable is differentiable if its derivative exists at each point in its domain. For real-valued functions of a real variable, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain. A differentiable function is locally approximable by a linear function at each interior point, and does not contain any break, angle, or cusp. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Differentiable functionA 5-minute orientation
  2. Skim a recent paper: Loss-of-function, gain-of-function and dominant-negative mutations have profoundly different effects on protein structureInfluential work since 2022
  3. Pick up a classic book: A course of modern analysisThe most-reprinted book on the subject
  4. Read the landmark paper: Minimizing a differentiable function over a differential manifoldCited 190 times
  5. Go sideways: Cauchy–Riemann equationsA closely related topic
  6. Go sideways: Fréchet derivativeA closely related topic

📖 Definitions

No dictionary entry for this exact phrase.

🗂️ The subject at a glance

  1. Differentiability of real functions of one variable
  2. Differentiability and continuity
  3. Differentiability classes
  4. Differentiability in higher dimensions
  5. Differentiability in complex analysis
  6. Differentiable functions on manifolds

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics