the derivative, $$\frac{dy}{dx} = \frac{y(x+dx)-y(x)}{(x+dx)-x} = \frac{y(x+dx)-y(x)}{dx}
\label{eq:deriv}$$

[**IMPORTANT NOTE**]{} Many textbooks, for historical reason, write the derivative of a function $y(x)$ with a “prime” symbol. So the symbols $y',
y(x)', y'(x), \mbox{and}\,\frac{dy}{dx}$ all mean exactly the same thing. I shall sometimes use the prime symbol in this article, so that students can accustom themselves to both usages.

[**EXERCISE**]{}

[**2.3**]{} Redo Exercise 2.1, this time using the dibbl method.

POWERS OF SMALL NUMBERS;\
THE DIBBL dx
-------------------------

We have introduced the dibbl as a quantity “that is so small that its square is as good as zero”. “How small is that?”, you might say. So let’s get some experience with the squares of small numbers.

[**EXERCISE**]{}

[**2.4**]{} You may use your calculator for this exercise:\
(a) How much is the square of $\frac{1}{5}$? (Hint: If you didn’t get $\frac{1}{25}$, ask your teacher to send you back to third grade).\
(b) Now take a piece of paper and a ruler marked in centimeters and draw a straight line that is 10 cm long. Divide the line into 5 equal parts by marking little perpendicular lines (“tick marks”) on the line, like the longer vertical lines in Fig. 1.\
Next, divide each 