I was reading H. Jerome Keisler's Elementary Calculus: An Infinitesimal Approach, chapter 1.4 ("Slope and Velocity: The Hyperreal Line") (PDF here). Page 23 explains getting the derivative of a function by finding Δy/Δx. It explains that, at the end, we "neglect the term Δx because it is very small."
However, when I was deriving $y=x^2+4$, I ended up with $\Delta y/\Delta x = 2x_0 + \Delta x + 4/\Delta x$. If $\Delta x$ is "very small," then instead of neglecting $4/\Delta x$, shouldn't it be infinity (as 4/0.000001 is 4 million, etc.)?
If it matters, I haven't even taken Pre-calc yet (I'm in Algebra II/Trig right now).