The Derivative Function and Interpretations of the Derivative

The most difficult part of sections 2.2 and 2.3 was Lebniz's notation. In high school I had seen derivatives as f'(x)= dy/dx but i had never known that the notation was to indicate that the derivative is a limit of ratios. Just by using multiple notations to imply the same point [the derivative of a function] gets cofusing. I am kind of wondering why Gottfried Wilhelm Leibniz felt the need to use d instead of delta?

I think the class will have to work through estimating derivative values from looking at a graph. I mean the derivative is the slope of the tangent line of a point on that graph, but its not as easy as it sounds. Also looking at graphs everybody will need to be able to predict how a graph of f'(x) will look depending on f(x)

By the way, as we progress though the examples in the book, i am finding more biological uses for math and that's pretty exciting since its connecting math to something very important/interesting to me. See example 8- health care costs or problem 37-diaphragm pressure.