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 December 18th, 2012, 01:33 PM #1 Newbie   Joined: Dec 2010 Posts: 17 Thanks: 0 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: $S(r)=\pi r^2$. 2. The length of a circle is radius function: $l(r)=2 \pi r$. 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:$\Delta r \to 0=dr$. 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:$d \pi r^2=2 \pi r \cdot dr$ (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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