Tag: differential

# Derivatives Explained (Part 1)

A couple of weeks ago, I posted the intro to this series. This is part 1 of this series, where I will throw light upon the basic rules of derivatives. But before you continue, make sure that you understand the concept(s) explained in the intro post. Then you may continue on to this post.

We know that taking a derivative is easy with simple functions, and sometimes linear functions. But when it is almost impossible to calculate without guides, you have to refer to rules. The basic rules are: (Note: $c$ refers to any constant, and $f(x)$ and $g(x)$ refer to functions.)

$(c \times f(x))' = c \times f(x)'$

$f(x) = g(x) + c$ $f(x)' = g(x)'$ or in other words, $(c)' = 0$

and lastly (for now) $f(x) = n^m$ $f(x)' = mn^{m-1}$

If you combine this knowledge with algebraic rules such as $n^an^b = n^{a+b}$ or $x^{-1} = \frac{1}{x}$

### Sidenote:

$\frac{d}{dx} f(x)$ is the same as $f(x)'$. I use the notation with the apostrophe because it is shorter and simpler. If the first notation is used anywhere, know that that is a derivative. End Sidenote

With this information, you can (and will) solve almost all functions excluding ones that use the exponential function, logarithms, trig, etc. To test your knowledge, I recommend you solve some tests on this topic. One of the resources available on this topic are MAT 270 calculus tests. I don’t exactly know the origin, but I think these resources are provided by Arizona State University, but I’m not sure.

This is it for this blog post, I hope I explained it well. As I said, I highly recommend practicing derivatives to have learned the topic. Take care!

A derivative is a function $f'(x)$, that gives the slope of the function $f(x)$. To signify a derivative, an apostrophe is put in front of the function name, for example $tax(x) \rightarrow tax'(x)$