Fundamental Functions





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02) Differentiation: Basic Rules

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There are many "Rules" of differentiation, but in a sense these are shorthand which skip over the complicated proof that show why they work. Although, at the level of IGCSE these proofs are unnecessary to be placed in each question they are used, and can be assumed to be true when used, enough paper is used as it is. However, I do encourage to look and attempt to understand the proof, as it is a useful method for remembering the how and when to use them. The proof of each can be seen through the link to the eventual page for it:  Here The first rule, is known as the Power Rule, since it deals with functions of x by the power of a non-variable value. For example: f(x)^n. Can be differentiated by reducing the power by 1, and multiplying by the power and the derivative of f(x). The second rule, is known as the Reciprocal Rule, since the reciprocal of f(x) is 1/f(x) or (f(x))^(-1). In fact, this rule is formed by the Power Rule, however remembering this as it is, is fine, The thi...
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01) 2D Vector: Fundamentals

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Where Vector means " determining the position of one point in space relative to another". Things to note: 1) While not always the case, Point O is usually considered the origin point, meaning that it's position in 2 dimensional space is (0,0). 2) Due to the limitations of digital text, any Vector going by the naming convention of XY where X and Y are points, implies a Vector Line from Point X to Point Y. Where it would usually look, for OA, like: 3) Vector Lines can be added together, the rule being that the end point of one must be the beginning point of the next, for example: OA + AB = OB, since OA is the vector from Point O to Point A, then AB is the vector from Point A to Point B, adding them together creates a vector that goes from Point O to Point A to Point B. 4) Vectors can also be denoted in a Variable-like fashion, for example OA can be denoted as "a". Thus these Vectors can be arranged in an equation to form the Vector of one point to another. For exa...
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