Math Methods – Differentiation 1/5

January 4, 2021grusha

In this short course, I will give you all the tips you need to succeed at differentiation. It is extremely important to practice, practice, practice… No one ever got good at math by just reading. In class, you will learn what differentiation is, so we are simply going to focus on technique. That said, let’s get started.

Notation & Vocabulary

If we wish to differentiate a function f(x), we are looking for its derivative and we write it as f’(x) – and we read “f prime of x”.


The derivative of any number (whether positive or negative, a fraction, a square root, even pi) is simply 0. So if :

f(x) = -12.7  then  f’(x) = 0

The derivative of axn (where a and n are random numbers) is naxn-1

That might seem complicated but really isn’t… Simply multiply by the power, then bring the power down by one unit. Here’s a couple of examples :

When you have addition or subtraction in the polynomial, you can simply differentiate each term one by one.


Ok, now that polynomials are under control, you simply need to remember that the derivative of sin(x) is cos(x), and the derivative cos(x) is -sin(x). Notice the negative sign which isn’t a typo, it’s really annoying, I know, but that’s just the way it is. Make sure you remember this! Here’s a couple more examples, make sure you understand them :

That’s it for now! Even though I haven’t explained what derivatives are, or what their use is, don’t worry about that for now, just master the technique. You won’t regret it. Below are some exercises that I highly recommend. Get in touch if you need the solutions, but they shouldn’t be too hard. All the best!



About Learnmate

Learnmate is a trusted Australian community platform that connects students who want 1:1 or small group study support, with tutors who are looking to share their knowledge and earn an income. From primary school to high school subjects — from science and maths to niche subjects like visual communication — Learnmate can help you improve academic performance or boost confidence, at your pace with the tutor that you choose.

We pride ourselves in offering a reliable and positive experience for both our students and tutors. Every tutor that joins the platform is vetted to meet a level of academic excellence, teaching qualification or relevant experience. All tutors are provided the opportunity to complete professional training.

Students and parents can easily find and screen for tutors based on their location, their subject results or skill level, and whether they provide in-person or online sessions. Learnmate is proud to provide tutors in Melbourne, Sydney, Geelong, Brisbane, Hobart, Canberra, Perth & Adelaide, and other locations.

Go online and let Learnmate help you get ahead. Start your search today.

Share this post
Article Author


Background Divider
© Copyright Learnmate 2024
linkedin facebook pinterest youtube rss twitter instagram facebook-blank rss-blank linkedin-blank pinterest youtube twitter instagram