Differentiation

This course is a part of AP®︎ Calculus AB, a 10-course Topic series from Khan Academy.

The derivative of a function describes the function's instantaneous rate of change at a certain point. Another common interpretation is that the derivative gives us the slope of the line tangent to the function's graph at that point. Learn how we define the derivative using limits. Learn about a bunch of very useful rules (like the power, product, and quotient rules) that help us find derivatives quickly.

This course contains 12 segments:

Defining average and instantaneous rates of change at a point

Defining the derivative of a function and using derivative notation

Estimating derivatives of a function at a point

Connecting differentiability and continuity: determining when derivatives do and do not exist

Applying the power rule

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

Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule

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

The product rule

The quotient rule

Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions

Optional videos

Some things are not explicitly required by the AP Calculus AB course, but many teachers cover them and we also find them useful. We've gathered those optional videos here for your convenience.