Exponentials & Logarithms

Summary is known as an exponential function Logarithmic functions are written as Laws of logarithm: 1.     2.     3.     4.     5.     6.     Exponential functions When n is a positive integer and a is the base in , then n is known as the index, power or exponent. Suppose we have , this is called an exponential … Read more

Integration Techniques

Summary Integration techniques include: Integration of trigonometric functions:  Integration of exponential functions:  Integration of :   Integrating Fractions: This involves , numerator is the derivative of a function within the denominator and lastly partial fractions. We know that the process of antidifferentiation is called integration. Clearly if    then    where    is known as the … Read more

Integration by Substitution

Summary Substitution Rule is defined as: Indefinite Integral: Definite Integral: where   We often get an integral which does not correspond to any standard result mentioned earlier. We therefore choose a suitable new variable u to replace x. We also replace dx by du. If this substitution transforms the original integrand into a simpler integral … Read more

The Product and Quotient Rule

Summary The Product Rule Formula: The Quotient Rule Formula: Where f’(x) and g’(x) are derivatives of f(x) and g(x) respectively.   The Product Rule When we have to find the derivative of the product of two functions, we apply ”The Product Rule”. Let’s suppose we have two functions f(x) and g(x). We are required to … Read more

Tangents and Normals

Summary A tangent is a line that just touches the curve but doesn’t go through it. The gradient of a tangent = Gradient of a curve at that point A normal is a straight line perpendicular (at right angle 90°) to a curve. We know that differentiation is the process that we use to find … Read more

The Chain Rule

Summary Chain rule lets us differentiate a function of a function i.e  Chain rule can be applied through two different equations: AND What is the chain rule? One of the rules of differentiation is the chain rule, which basically lets us differentiate a function of a function in other words differentiation of composite functions. Let’s … Read more