It looks like a very nice careful description, but where is the physical intuition? Where's the plots of tangent lines on a function at various points?
There's nothing wrong with the article (I think), I am just curious about the pedagogy and motivation for not immediately introducing a graphical conceptualization of a derivative especially for such a "from the ground up" exposition.
Hi, author here. This is what made derivatives finally click for me (as opposed to the tangent line) so that’s how I wanted to explain it...maybe the same thing would click for others!
IMO it is more about drawing ability vs app knowledge, so I would suggest learning to draw! Just start drawing and you'll get better over time. You could join something like https://streak.club/s/8/daily-art to keep motivated.
That question mark is beautiful, and the thickness varies in a particular way that is quite unlike regular handwriting. It's more like chalk on a chalkboard. That's why I was hoping to know the exact settings.
I spent some time with the Procreate app today and was able to pick up the basics. I'll try learning by copying your work. Thanks again!
For what it's worth, I like this much better. I had the traditional method of graphs and tangents. I was slightly lost on it in Cal I, and I could regurgitate it in Cal II. "The derivative of a function is the amount of change of the output with respect to the input." This is another level of derivatives clicking
Hi author. There is a typo in the section How To Calculate The Derivative. The first two images in that section label 0.1^2 as "input change" in the denominator. It should be 0.1, not squared.
I do not really learn a concept until I can visualize it somehow. Indeed, when I was learning derivatives, it did not click until I saw a graph with a tangent line. But everybody is not the same way. Some people prefer to develop their intuition based on a text explanation, some people need an example with numbers, some other people need an actual person to explain it to them in spoken words.
When you learn better with one of these methods, seeing another one first may confuse you instead of helping. Moreover, once you have understand the concept, other kinds of explanations tend to broaden your view of the topic.
I think this a great non-visual explanation of derivatives. No more, but no less. I think it has a great pedagogical value, even if it is not the best introduction for my way of learning.
Reducing explanation of the derivative at an intuitive level to 'simply the rate of change' confuses the hell out of people when they encounter other things that are also defined as derivatives but do not describe a change in any obvious sense. For example, electric current (or, say, a flow of water) through a cross-section of a closed circuit does not necessarily represent a change of electic charge (or the mass of water) on either side of the surface, as it remains constant.
There's nothing wrong with the article (I think), I am just curious about the pedagogy and motivation for not immediately introducing a graphical conceptualization of a derivative especially for such a "from the ground up" exposition.