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December 18th, 2012, 01:33 PM   #1
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Geometrical interpretation of a derivative

If want to understand geometrical sense of a derivative, consider for a start such example:
1. The area of a circle is radius function: .

2. The length of a circle is radius function: .

3. These two functions of the same argument are connected with each other in a special way, namely, as a derivative-antiderivative.

4. The radius differential - is distance between the next points, - an elementary piece - the smallest radius what only can be:.

5. Increase of length of a circle on radius differential - is differential of the area of a circle - the smallest increment of the area of a circle which only can be: (elementary ringlet).

6. The area of a circle is the sum of all elementary ringlets, beginning from the center of a circle and to its any value, for example R: [math]\displaystyle \int\limits_0^R l(r)dr[/latex]
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