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Everything about Derivative

Instantaneous rate of change (mathematics)

In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. The derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable. The process of finding a derivative is called differentiation. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: DerivativeA 5-minute orientation
  2. Skim a recent paper: The application of mesenchymal stromal cells (MSCs) and their derivative exosome in skin wound healing: a comprehensive reviewInfluential work since 2022
  3. Pick up a classic book: The origin of continentsThe most-reprinted book on the subject
  4. Read the landmark paper: Polydopamine and Its Derivative Materials: Synthesis and Promising Applications in Energy, Environmental, and Biomedical FieldsCited 4,733 times
  5. Go sideways: Notation for differentiationA closely related topic
  6. Go sideways: Differential of a functionA closely related topic

📖 Definitions

Adjective Obtained by derivation; not radical, original, or fundamental.

Adjective Imitative of the work of someone else.

Adjective Referring to a work, such as a translation or adaptation, based on another work that may be subject to copyright restrictions.

Adjective Having a value that depends on an underlying asset of variable value.

🗂️ The subject at a glance

  1. Definition
  2. Continuity and differentiability
  3. Notation
  4. Rules of computation
  5. Antidifferentiation
  6. Higher-order derivatives
  7. In other dimensions
  8. Generalizations

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

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