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Chapter 3 · Grade 12 Advanced
Differentiation
The derivative measures instantaneous rate of change. This chapter develops the toolkit needed to differentiate any function you'll meet.
Lessons
Lesson 1 · G12 3.1
Tangent Lines and Velocity
From average to instantaneous rates.
Open lesson → Lesson 2 · G12 3.2The Derivative
Definition as a limit, notation, basic interpretation.
Open lesson → Lesson 3 · G12 3.3Computation of Derivatives the Power Rule
Differentiating powers efficiently.
Open lesson → Lesson 4 · G12 3.4The Product and Quotient Rules
Differentiating products and quotients.
Open lesson → Lesson 5 · G12 3.5The Chain Rule
Differentiating compositions.
Open lesson → Lesson 6 · G12 3.6Derivatives of Trigonometric Functions
Sin, cos, tan and their relatives.
Open lesson → Lesson 7 · G12 3.7Derivatives of Exponential and Logarithmic Functions
e^x, a^x, ln x, log_a x.
Open lesson → Lesson 8 · G12 3.8Implicit Differentiation and Inverse Trig
When y is not isolated.
Open lesson → Lesson 9 · G12 3.9The Hyperbolic Functions
Sinh, cosh and their derivatives.
Open lesson → Lesson 10 · G12 3.10The Mean Value Theorem
A pillar theorem of calculus.
Open lesson →