Unit 3: Differentiation: Composite, Implicit & Inverse Functions
Work through these 6 topics in order. Clear the gatekeeper and the rest of the course opens up.
3.1 The chain rule
A composite function is one function inside another.
3.2 Implicit differentiation
When an equation is not solved for y, treat y as a hidden function of x.
3.3 Differentiating inverse functions
An inverse function is the graph reflected across y=x, so its tangent slopes are RECIPROCALS of the original’s at the matching (reflected) point.
3.4 Derivatives of inverse trigonometric functions
The inverse-trig derivatives are clean algebraic expressions (no trig left) — memorize them, and apply the chain rule to any inner function.
3.5 Selecting procedures for derivatives
Before differentiating, read the STRUCTURE: is it a product, a quotient, a composite, or an implicit equation?
3.6 Higher-order derivatives
Differentiate again to get the rate of the rate.