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

Uses Of Differentiation

Summary If y = f(x) is an increasing function then  If y = f(x) is a decreasing function then  Stationary Points are obtained by solving the equation  3 types of stationary points: i) Maximum Point ii) Minimum Point iii) Point of Inflexion Increasing Function Refer to Fig 1, consider a point A on the curve … Read more

Differentiation From First Principle

Summary 4 steps to work out differentiation from the First Principle: Give increments to both x & y i.e . Find change of y. Find rate of change of y with respect to x i.e    or  . Take the limit of    as . Gradient of a curve We know that the gradient of … Read more

Integration By Parts

Summary Remember the formula for ‘Integration By Parts’: We now know how to evaluate many basic integrals. However there are many integrals which are in the form of two functions and cannot be simplified by any substitution. In such cases we use the ‘Product Rule’ of differentiation. We know that: Rewrite it as: Integrating both … Read more