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Chain Rule for Derivatives Let’s discuss the chain rule, which is really nothing more than the derivative of a composite function. What is the derivative of the sine of 3x? It is common to assume that the derivative of sine x is cosine x, because the inside part of the function does not change. However…

Geometry proofs using coordinate free vectors Euclidean geometry is a branch of geometry that deals with the theory of the relationship between points, lines and planes. It is one of the three classical branches of geometry, together with topology and trigonometry. The median of a triangle is the line segment that joins the midpoints of…

Review tangent approximation In this section, we are going to see how to use the partial derivatives. When we have a function of two variables, x and y, then we have, actually, two different derivatives: partial f, partial x, called f sub x. This is the derivative off with respect to x while keeping y…

CFA Level 3 – Ethical and Standards, Session 2 – Reading 6 (Notes, Practice Questions, Sample Questions) 1. Which of the following is NOT part of the ethical responsibilities related to the Asset Manager Code of Professional Conduct? A) Act in an objective manner.B) Communicate with clients in an accurate manner.C) Do not engage in…

Cartesian Plane: Slope-Intercept Formula for Lines We will now derive the equation of a line using the point slope formula. The line we are working with passes through the point (2,1) and has a slope of M=1. Therefore. the point slope formula of the line is y-1= 1(x-2). Any point (x,y) that wants to be…

Scalar multiplication Scalar multiplication of vector is a process of multiplying a vector by a scalar. A scalar is a number that does not depend on any other quantity in the equation. Scalar multiplication does not change the direction, just the length of a vector. Lambda of a vector is the scalar value that corresponds…

Simplification Rules The simplification rules are used to simplify expressions. These rules help us to get rid of some of the extra steps that are required when simplifying an expression. The main idea behind these rules is to simplify an expression by combining like terms, grouping terms together and canceling variables. To simplify an expression…

Using Integer Exponents Positive integer exponents are a notation to express a number raised to any given power. They are defined as a superscripted number. The number above the base is called the exponent and is used to represent a power of the base. For example, 2^4 = 2 * 2 * 2 * 2…

CFA Level 3 – Fixed Income, Session 10 – Reading 24 (Notes, Practice Questions, Sample Questions) 1. Which of the following best describes the basis for relative-value analysis? A)Generates rankings of expected returns. {Explanation — Relative value refers to the ranking of fixed-income investments by sectors, structures, issuers, and issues in terms of their expected…

Extrema on an Interval Where is the highest, where is the lowest point on a curve? The highest point on a curve is called the peak. The lowest point on a curve is called the trough. The highest and lowest points are also called the extrema of a curve, or simply extremas. Let’s talk about…