Differential Calculus videos

Limits intro

Estimating limits from graphs

Estimating limits from tables

Formal definition of limits (epsilon-delta)

Properties of limits

Limits by direct substitution

Limits using algebraic manipulation

Strategy in finding limits

Squeeze theorem

Types of discontinuities

Continuity at a point

Continuity over an interval

Removing discontinuities

Infinite limits

Limits at infinity

Intermediate value theorem

Average vs. instantaneous rate of change

Secant lines

Derivative definition

Estimating derivatives

Differentiability

Power rule

Derivative rules: constant, sum, difference, and constant multiple

Combining the power rule with other derivative rules

Derivatives of cos(x), sin(x), 𝑒ˣ, and ln(x)

Product rule

Quotient rule

Derivatives of tan(x), cot(x), sec(x), and csc(x)

Proof videos

Chain rule

More chain rule practice

Implicit differentiation

Implicit differentiation (advanced examples)

Differentiating inverse functions

Derivatives of inverse trigonometric functions

Strategy in differentiating functions

Differentiation using multiple rules

Second derivatives

Disguised derivatives

Logarithmic differentiation

Proof videos

Meaning of the derivative in context

Straight-line motion

Non-motion applications of derivatives

Introduction to related rates

Solving related rates problems

Approximation with local linearity

L’Hôpital’s rule

L’Hôpital’s rule: composite exponential functions

Mean value theorem

Extreme value theorem and critical points

Intervals on which a function is increasing or decreasing

Relative (local) extrema

Absolute (global) extrema

Concavity and inflection points intro

Analyzing concavity and inflection points

Second derivative test

Sketching curves

Connecting f, f', and f''

Solving optimization problems

Analyzing implicit relations

Calculator-active practice

Parametric equations intro

Second derivatives of parametric equations

Vector-valued functions

Planar motion

Polar functions