Does anyone know a good online course, free, which teaches the Derivative and its geometry?
try this http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/video-lectures/
and this https://www.khanacademy.org/math/differential-calculus/taking-derivatives
There is an old series i found to be awesom, besides the two linked above... its called calculus revisited, it is also on MIT OCW, but it is from Herbert Gross in like 1950's, Best lectures i think .
If you prefer reading text, here's a link for some PDF downloads. If you're only interested in differentiation, then chapters 1-4 should suffice. http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/
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