Calculus Archive

Products, Quotients, and Chains: Simple Rules for Calculus

In this post, we are going to explain the product rule, the chain rule, and the quotient rule for calculating derivatives. We derive each rule and demonstrate it with an example. The product rule allows us to differentiate a function that includes the multiplication of two or more variables. The quotient rule enables us

Differential Calculus: How to Find the Derivative of a Function

In this post, we learn how to find the derivative of a function from first principles and how to apply the power rule, the sum rule, and the difference rule. We previously established that the definition of a derivative equals the following expression. Note that f'(x) is a more compact form to denote the

Rise Over Run: Understand the Definition of a Derivative

We introduce the basics of calculus by understanding the concept of rise over run, followed by a more formal definition of derivatives. At the heart of calculus are functions that describe changes in variables. In complex systems, we usually deal with many changing variables that depend on each other. The concept of rise over