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ExploreCalculusDifferentiation: definition and basic derivative rules

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Calculus

Differentiation: definition and basic derivative rules

  • Defining average and instantaneous rates of change at a point
  • Defining the derivative of a function and using derivative notation
  • Estimating derivatives of a function at a point
  • Connecting differentiability and continuity: determining when derivatives do and do not exist
  • Applying the power rule
  • Derivative rules: constant, sum, difference, and constant multiple: introduction
  • Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule
  • Derivatives of cos(x), sin(x), 𝑒ˣ, and ln(x)
  • The product rule
  • The quotient rule
  • Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions

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