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Ch 19 Differentiation

VIDEOS ON FIRST PRINCIPLES DIFFERENTIATION
Click on the link to go to a video on First Principles Differentiation
https://www.youtube.com/watch?v=hOlRskjmwbQ

This video goes through the fundamental concept of First Principles  Differentiation
https://www.youtube.com/watch?v=QEsoUxt2Zig

This video goes through an example of differentiating a function from first principles
https://www.youtube.com/watch?v=bjScSwthZZs
This video goes through through an example of establishing the gradient of the tangent using First Principles
https://www.youtube.com/watch?v=PXwVLvAWBzE

VIDEOS ON SKETCHING THE DERIVATIVE FUNCTION
This video explains the principles behind sketching the derivative function from the properties of the original function
https://www.youtube.com/watch?v=Gbtma_UQpro

Here is another video that explains how to sketch the graph of the derivative function from the original function
https://www.youtube.com/watch?v=uJC-eobULME

Here is another video that explains the relationship between the original function and the graph of its derivative with a matching exercise.
https://www.youtube.com/watch?v=dHFChPQMX4s

VIDEOS ON CONTINUITY of FUNCTIONS and DIFFERENTIABILITY OF FUNCTIONS (Ex 19D and Ex 19E)
Here is a link to a really excellent set of small tutorials that explain simply and clearly the concepts of LIMITS, and CONTINUITY  (Ex 19D). Tutorials 1 to 5 are all relevant.
http://www.calculus-help.com/tutorials
Here is a short and clear video that explains when a function is continuous.
https://www.youtube.com/watch?v=DJP2sAVpu8k

Here is another video that clearly explains the ideas behind continuity.
https://www.youtube.com/watch?v=nqD17if3Znw

Here is an excellent video that explains when  a function is differentiable. It has Beatles music as well!!
https://www.youtube.com/watch?v=Ei9p_h0mL_w