So, there I was during IRC, just chatting along, when someone asked some random calculus question, I got it right, and then they asked me to explain how to do derivatives the “easy” way. I was originally going to do this through MSN Messenger with the nifty little drawing conversation feature, but alas, the person in question didn’t support Handwriting. Instead, I’m now going to make a short little blog post about how one can easily do a derivative. This is just the easy stuff, remember, I’m not getting into derivatives of fractional functions or something like that.
Another thing, these graphical examples were done quickly in paint, so don’t make fun of me ;_;
First, we have a simple function f(x) = x^2 – 3x – 4, as displayed in the picture below:
For simple derivatives such as these, we first have to remember some properties of exponents, such as: any variable by itself (or with a coefficient) is variable^1 . If a coefficient is by itself, we can say that it the coefficient multiplied times the variable to the zeroeth power — variable^0 . We can use these properties to modify our original equation to look something like this:
Now that we have the modifications out of the way, we can get to the actual derivation. For equations like these, to get the derivative, you multiply the power by the coefficient, and then subtract one from the power, as shown in the drawing:
Then, you use a bit of simplification, and you’ll come out with f‘(x) = 2x – 2, as shown below:
See? It’s not really that hard. :)