We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).Differentiation is also used in analysis of finance and economics.

In this unit students will analyze and manipulate functions in order to apply them to real-life optimization (minimum/maximum) situations.

This is a lesson on finding the difference between an implicit and explicit function and finding the derivative of functions implicitly. It also covers finding the equation of a tangent line from a function in implicit form . There are self check throughout the lesson. The text that I use in my calculus class is Larson Calculus 11th edition. This corresponds to chapter 2 section 5 in that text but Implicit Differentiation is a common topic in any Calculus I or AP Calculus course.

This 9-minute video lesson provides an introduction to L'Hopital's Rule. [Calculus playlist: Lesson 36 of 156]

CK-12's Texas Instrument Calculus Student Edition is a useful companion to a Calculus course, offering extra assignments and opportunities for students to understand course material through their graphing calculator.

CK-12's Texas Instruments Calculus Teacher's Edition is a useful companion to a Calculus course, offering extra assignments and opportunities for students to understand course material through their graphing calculator.

This series of videos focusing on calculus covers calculating derivatives, power rule, product and quotient rules, chain rule, implicit differentiation, derivatives of common functions.

You can take the derivatives of f(x) and g(x), but what about f(g(x)) or g(f(x))? The chain rule gives us this ability. Because most complex and hairy functions can be thought of the composition of several simpler ones (ones that you can find derivatives of), you'll be able to take the derivative of almost any function after this tutorial. Just imagine.

Discover what magic we can derive when we take a derivative, which is the slope of the tangent line at any point on a curve.

The topic that is now known as "calculus" was really called "the calculus of differentials" when first devised by Newton (and Leibniz) roughly four hundred years ago. To Newton, differentials were infinitely small "changes" in numbers that previous mathematics didn't know what to do with. Think this has no relevence to you? Well how would you figure out how fast something is going *right* at this moment (you'd have to figure out the very, very small change in distance over an infinitely small change in time)? This tutorial gives a gentle introduction to the world of Newton and Leibniz.

We told you about the derivatives of many functions, but you might want proof that what we told you is actually true. That's what this tutorial tries to do!

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 1 covers functions, limits, derivatives, and integration

Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course.

This 12-minute video lesson looks at useful properties of the Laplace Transform. [Differential Equations playlist: Lesson 30 of 45]

Thompson Rivers University (TRU) has developed an OER in financial management consisting of 21 learning modules that can be used to teach courses in introductory and advanced financial management at the undergraduate and graduate levels as well as a course in business valuations. Each module consists of a detailed reading, presentation slides, learning problems, and answer keys. A number of case studies in areas such as financial statement analysis, financing planning, capital budgeting, and cost of capital are also included along with sample course outlines.

Faculty can select whatever modules they feel are needed to achieve the specific learning outcomes for a course. As OERs, faculty are also free to modify the readings, problems, or case studies so they better meet their needs and those of their students. These modules can be quickly imported into a learning management system such as Moodle or Blackboard to produce a challenging face-to-face or online learning experience.

With the rising cost of education, particularly textbooks, faculty are obligated to “adopt and adapt” OERs whenever possible to help their students.

The following notes and practice problems are ancillary materials for OpenStax Calculus Volume 1. Topics include:

Limit of a Function
Continuity
Derivatives
Differentiation

This is a course in how corporations make use of the insights and tools of risk management. Most courses on derivatives, futures and options, and financial engineering are taught from the viewpoint of investment bankers and traders in the securities. This course is taught from the point of view of the manufacturing corporation, the utility, the software firm—any potential end-user of derivatives, but not the dealer. Most related courses focus on the extensive taxonomy of instruments and the complex models developed to price them, and on ways to exploit mispricing. While this course will make use of some of these pricing models, the focus is on how corporations use the insights and models to improve their operations, to increase the value of their real assets, or to create the financial flexibility necessary to implement their core strategy.