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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