Applications of derivatives

This course is a part of Differential Calculus, a 6-course Topic series from Khan Academy.

Derivatives describe the rate of change of quantities. This becomes very useful when solving various problems that are related to rates of change in applied, real-world, situations. Also learn how to apply derivatives to approximate function values and find limits using L’Hôpital’s rule.

This course contains 8 segments:

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

L'Hôpital's rule provides us with an easy, almost magical way of finding indeterminate limits of quotients of functions using the functions' derivatives. In short, the rule says that if the limits of functions f and g at x=a are 0 (or ထ) and the limit of f'(x)/g'(x) at x=a is equal to L, then the limit of f(x)/g(x) at x=a is also equal to L.