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This lecture introduces differential calculus — the mathematics of rates of change — building from the slope of a line to the formal definition of the derivative and key differentiation rules.

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📋 At a Glance

• [ ] Understand the slope as a measure of rate of change
• [ ] Derive the formula for slope using Δx notation
• [ ] Distinguish between average and instantaneous rate of change
• [ ] Understand the formal definition of the derivative using limits
• [ ] Know the relationship: differentiability implies continuity (but not vice versa)
• [ ] Apply the derivative definition from first principles (Example 1)
• [ ] Memorise key derivative rules: constant, power, exponential, logarithmic
• [ ] Apply the sum, difference, and constant multiple rules
• [ ] Apply the product rule and quotient rule
• [ ] Understand what the sign of the derivative tells us about a function
• [ ] Apply the chain rule for composite functions
• [ ] Handle derivatives involving absolute values
• [ ] Understand implicit differentiation basics
• [ ] Find higher-order derivatives (second derivative)

1. Rate of Change (Review)

Slope of a Line