If you are connected to any kind of financial market or watch the financial news even for 5 minutes every day, it is likely that you have heard the word, financial derivatives many times. The media is flush with articles wherein derivatives are criticized or appreciated. Most of the times, commentators are in awe of the mind-numbingly large amounts behind these contracts. It is often said that the total amount of derivatives contracts in the worlds, is actually greater than the total amount of money available in the world!
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Derivatives In this chapter we will start looking at the next major topic in a calculus class, derivatives. This chapter is devoted almost exclusively to finding derivatives. We will be looking at one application of them in this chapter.
We will be leaving most of the applications of derivatives to the next chapter. Here is a listing of the topics covered in this chapter. The Definition of the Derivative — In this section we define the derivative, give various notations for the derivative and work a few problems illustrating how to use the definition of the derivative to actually compute the derivative of a function.
Interpretation of the Derivative — In this section we give several of the more important interpretations of the derivative.
We discuss the rate of change of a function, the velocity of a moving object and the slope of the tangent line to a graph of a function. Differentiation Formulas — In this section we give most of the general derivative formulas and properties used when taking the derivative of a function.
Examples in this section concentrate mostly on polynomials, roots and more generally variables raised to powers. Product and Quotient Rule — In this section we will give two of the more important formulas for differentiating functions.
We will discuss the Product Rule and the Quotient Rule allowing us to differentiate functions that, up to this point, we were unable to differentiate. Derivatives of Trig Functions — In this section we will discuss differentiating trig functions.
Derivatives of Exponential and Logarithm Functions — In this section we derive the formulas for the derivatives of the exponential and logarithm functions.
Derivatives of Inverse Trig Functions — In this section we give the derivatives of all six inverse trig functions. We show the derivation of the formulas for inverse sine, inverse cosine and inverse tangent. Derivatives of Hyperbolic Functions — In this section we define the hyperbolic functions, give the relationships between them and some of the basic facts involving hyperbolic functions.
We also give the derivatives of each of the six hyperbolic functions and show the derivation of the formula for hyperbolic sine.
Chain Rule — In this section we discuss one of the more useful and important differentiation formulas, The Chain Rule. With the chain rule in hand we will be able to differentiate a much wider variety of functions.
As you will see throughout the rest of your Calculus courses a great many of derivatives you take will involve the chain rule! Implicit Differentiation — In this section we will discuss implicit differentiation.
Not every function can be explicitly written in terms of the independent variable, e. Implicit differentiation will allow us to find the derivative in these cases. Knowing implicit differentiation will allow us to do one of the more important applications of derivatives, Related Rates the next section.
In related rates problems we are give the rate of change of one quantity in a problem and asked to determine the rate of one or more quantities in the problem. This is often one of the more difficult sections for students. We work quite a few problems in this section so hopefully by the end of this section you will get a decent understanding on how these problems work.
Higher Order Derivatives — In this section we define the concept of higher order derivatives and give a quick application of the second order derivative and show how implicit differentiation works for higher order derivatives.
Logarithmic Differentiation — In this section we will discuss logarithmic differentiation. Logarithmic differentiation gives an alternative method for differentiating products and quotients sometimes easier than using product and quotient rule. More importantly, however, is the fact that logarithm differentiation allows us to differentiate functions that are in the form of one function raised to another function, i.1.
Take derivative 2. Plug given x value into derivative (for slope) 3. Negative reciprocal of slope 4. Plug into point-slope form. Study Guide Resource Home Textbook Instructor's Manual Study Guide Computing in Calculus (PDF - MB) 2: Derivatives.
The Derivative of a Function Powers and Polynomials The Slope and the Tangent Line. Calculus Here is a list of skills students learn in Calculus!
These skills are organized into categories, and you can move your mouse over any skill name to preview the skill. Beginner’s Guide to NCFM Certification Exam:If you are considering undertaking NCFM modules, there are a lot many of them to caninariojana.com of course cannot consider giving all of them at the same time.
Here through this article, I wish to provide you with a brief summary on their modules which might help you decide which one you should choose from. Aug 07, · Derivatives Essentials: An Introduction to Forwards, Futures, Options, and Swaps (Wiley, ) by Aron Gottesman is an excellent textbook/self-study guide.
It . will use the product/quotient rule and derivatives of y will use the chain rule. The “trick” is to The “trick” is to differentiate as normal and every time you differentiate a y you tack on a y ′ (from the chain rule).
View Test Prep - DERIVATIVES study guide from ACCT I S at University of Wisconsin. DERIVATIVES Derivative financial instruments have become the key tools of RISK MANAGEMENT. Derivatives financial. The project that you can use to engage the students is to use word art as a way of creating a study guide of some sort. There are several terms associated with derivatives, so good way to remember the key terms would be to write the most important terms from . Calculus 1 Class Notes, Thomas' Calculus, Early Transcendentals, 12th Edition Copies of the classnotes are on the internet in PDF format as given below. Introduction to .