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”.
Polynomials
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.
Trigonometry
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!
Exercises
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