10 resources.
The chain rule in function and Leibniz notation, a table of standard chain-rule derivatives, four worked examples and common mistakes.
The power rule for whole, negative and fractional exponents, with a table of examples, two worked examples, a graph of x³ and its derivative, and common mistakes.
The product rule for two and three functions, logarithmic differentiation, worked examples and common mistakes.
The quotient rule with worked examples: a rational function, a derivative from given values, the derivatives of tan x and sec x, finding where the slope is zero, and common mistakes.
Derivatives as rates of change: a summary of every application, worked examples on area, velocity and related rates, and common mistakes.
Implicit differentiation step by step, with worked examples on product terms, second derivatives and an inverse trig identity, plus common mistakes.
Finding where a function increases or decreases from the sign of its derivative, with a sign chart, a graph, worked examples and common mistakes.
Rolle's theorem and the mean value theorem: conditions, graphs, a side-by-side comparison, worked examples and when the theorem fails.
Slopes and equations of tangent and normal lines to a curve, special cases, five worked examples including a tangent parallel to a given line, a graph and common mistakes.
Approximating values with differentials, why dy approximates Δy (with a graph), worked examples on roots, volume and error, and common mistakes.