# Category Archives for "Calculus"

## Desmos: A Definitive Guide (How to Perform Cool Computations and Creating Great Graphs Using Online Graphing Calculator)

Think you’re fond of of graphing and computing stuffs? Great! Because you might remember this thing called the Texas Instrument TI-83 from the old days. Sure, while programmable calculators in general are still pretty much popular these days, the graphing calculators from the 21st-century are also coming in waves as we speak — potentially disrupting the market of scientific computing and educational […]

## Infinite Limits and the Behaviors of Polynomials at the Infinities — A Theoretical Musing

Regardless of your early surrounding or schooling background, we know for one that there are two kinds of mathematical objects that are kind of hard to miss in life. The names? Polynomial and Infinity! While the former might have sounded a bit like the name of a snake, polynomials is a one-of-its-kind mathematical entity whose perfection defies our mathematical imagination. For […]

## Chain Rule for Derivative — Venturing Into The Dark Side Beneath Applied Calculus…

To the surprise of many math enthusiasts and the like, it seems that we have been pulling out on an incredible amount of calculus modules these days. Of course, if you have had any terrible experience in learning just the mechanics of calculus, this seemingly-relentless outpouring of materials could make you want to puke. However, if that header […]

## The Exponent Rule for Derivatives — Your One-Stop Shop to Staircase-Looking Functions

Like the featured image above? Good for you! As students (fanatics?) of mathematics and other technical sciences, we have an intuitive appreciation of the role this topic — calculus — plays out in our daily life. While obviously not a subject to be mastered overnight, what’s true is that our first exposure to it tends to be […]

## The Ultimate Guide to Logarithm — Theory & Applications

For the very vast majority of humans on earth, there is a topic found in the good old math textbooks that many of us still even dread contemplating about, as it seems to mess with our brain in a rather particular way.  The name? $\displaystyle \text{Logarithmus}$ — or Logarithm in English to be sure! As terrible-sounding as it […]

## Integration Technique Series — How to Make Use of the Overshooting Method and Integrate with Ease

Hey! Greeting from a bunch of post-April-Fool bunnies who never managed to get their modules published on time — because they were simply too busy eating Easter eggs and shooting for the moon.  🙂 Moving onto a more serious topic though, if you’re currently into (or have been into) this thing called integral calculus, you might know from first-hand […]

## Derivative of Inverse Functions (a.k.a, How to Create Your Own Table of Derivatives)

Quick question. Are you currently (or have been) a student of differential calculus (a.k.a., Calculus I)? If so, maybe you can guess what is on that (potentially-cryptic) graph above? What. Inverse functions of course! Just look at that beautiful shape and how well they correspond with each other! (OK. Bonus point: can you guess which […]

## Derivative of $x^x$, $x^{x^x}$, and a Venture Into Tetration and Hyper-Exponentiation

In a first course of calculus, we have very specific rules for dealing with functions in the form of a sum, a difference, a product and a quotient. And now, we’re about to throw a curve ball at you: What is the derivative of the function $f(x)=x^{x^x}$? Intrigued? Well, it’s time to learn more! For […]