Unit route
Study lessons in order, complete the pathway selected by diagnostic evidence, conduct the investigation, then demonstrate mastery. Reassessment follows correction and reflection.
Weeks 13, 14, 15 · 8 detailed lessons
Differentiation Rules & Higher Derivatives
How do derivative rules make complex rates of change efficient, interpretable, and verifiable?
Pathways
Lesson 01 · Week 13
Constant, Power & Sum Rules
Differentiation rules compress repeated limit arguments into reliable structures. Each rule should be chosen from the algebraic form of the function and verified through units, graph behavio…
Lesson 02 · Week 13Product Rule
Differentiation rules compress repeated limit arguments into reliable structures. Each rule should be chosen from the algebraic form of the function and verified through units, graph behavio…
Lesson 03 · Week 13Quotient Rule
Differentiation rules compress repeated limit arguments into reliable structures. Each rule should be chosen from the algebraic form of the function and verified through units, graph behavio…
Lesson 04 · Week 14Derivatives of Sine and Cosine
Trigonometric derivatives connect periodic position with periodic rates. Angle measure must be in radians for the standard derivative formulas to hold without an additional conversion factor…
Lesson 05 · Week 14Derivatives of Other Trigonometric Functions
Trigonometric derivatives connect periodic position with periodic rates. Angle measure must be in radians for the standard derivative formulas to hold without an additional conversion factor…
Lesson 06 · Week 14Derivatives of Exponential Functions
Exponential derivatives preserve exponential structure. The natural exponential function is its own derivative; other bases introduce a logarithmic scale factor.…
Lesson 07 · Week 15Derivatives of Logarithmic Functions
Logarithmic derivatives convert multiplicative structure into reciprocal rates. Domain restrictions remain essential because real logarithms require positive arguments.…
Lesson 08 · Week 15Higher-Order Derivatives and Motion
Position, velocity, and acceleration are successive layers of change. Their signs and zeros describe direction, speed changes, turning, and concavity, while their units distinguish the quant…