Derivatives

This course is a part of Differential Calculus, a 6-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 13 segments:

Average vs. instantaneous rate of change

Secant lines

Gain some experience working with secant lines. This will help us on our journey to find a formal definition for the derivative.

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), ?ˣ, and ln(x)

Product rule

Quotient rule

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

Proof videos