Finding Higher-Order Derivatives
Learn how to find second, third, and higher-order derivatives using a clear step-by-step method with fully worked examples for AP Calculus AB & BC.
Estimating Derivatives from Tables and Graphs
Learn how to estimate derivatives from tables and graphs using secant slopes, nearby values, tangent lines, and centered differences for AP Calculus AB & BC.
Derivatives of Trigonometric Functions: Tangent, Cotangent, Secant, Cosecant
Learn the derivatives of tangent, cotangent, secant, and cosecant, with identities, sign patterns, chain rule examples, and AP Calculus practice problems.
Derivatives of Trigonometric Functions: Sine and Cosine
Learn the derivatives of sine and cosine functions, including compositions with the chain rule, with step-by-step examples for AP Calculus AB & BC.
Derivatives of Piecewise-Defined Functions
Learn how to differentiate piecewise-defined functions, test differentiability at breakpoints, and solve AP Calculus AB & BC problems involving continuity and derivatives.
Derivatives of Natural Logarithmic Functions
Learn how to differentiate natural logarithmic functions, including ln(x), ln(u), logarithmic compositions, and applications of the chain rule for AP Calculus AB & BC.
Derivatives of Exponential Functions
Learn how to differentiate exponential functions including e^x, a^x, and exponential compositions, with step-by-step examples for AP Calculus AB & BC.
Derivative Rules: Constant, Sum, and Difference Rules
Learn the constant, sum, and difference rules for derivatives with a clear step-by-step method and fully worked AP Calculus examples.
Defining the Derivative of a Function at a Point
Learn how the derivative of a function at a point is defined using the limit of the difference quotient, with step-by-step examples for AP Calculus AB & BC.
Defining Average and Instantaneous Rates of Change
Learn how to define and calculate average and instantaneous rates of change, secant and tangent slopes, and the derivative from first principles for AP Calculus AB & BC.