Where Functions Are Not Differentiable: Corners, Cusps, and Vertical Tangents
Learn where functions are not differentiable, including corners, cusps, vertical tangents, discontinuities, and piecewise functions, with step-by-step AP Calculus examples.
Using the Limit Definition to Derive the Power Rule
See how the limit definition of the derivative leads directly to the power rule, with step-by-step derivations and fully worked examples for AP Calculus AB & BC.
The Quotient Rule Explained
How the quotient rule works, when to use it, and how to differentiate rational functions step by step with fully worked AP Calculus AB & BC examples.
The Product Rule Explained
Learn how the product rule works, when to use it, and how to differentiate products of functions with fully worked AP Calculus AB & BC examples.
The Derivative as a Rate of Change in Context
Understand the derivative as a rate of change in context, with units, interpretation, and fully worked AP Calculus AB & BC examples.
The Derivative as a Function
Understand the derivative as a function, how the difference quotient becomes f
Tangent Line Approximations from First Principles
Learn how tangent line approximations are derived from first principles and how to use linearization to estimate function values in AP Calculus AB & BC.
Practice Problem Set: Differentiation Basics
A focused AP Calculus practice problem set covering the fundamentals of differentiation, including derivative definitions, basic derivative rules, tangent lines, and rates of change.
Interpreting the Meaning of a Derivative in Context
Learn how to interpret the meaning of a derivative in context, including units, signs, rates of change, and AP Calculus free-response examples.
Graphing , , and Together
Learn how to connect the graphs of f, f-prime, and f-double-prime using increasing/decreasing behavior, extrema, concavity, and inflection points for AP Calculus AB & BC.