Animations of Derivative

Animation of a definition of derivative Animation of a definition of derivative
The above animations show two separate ways in which the derivative can be defined.

On the left we have
Limit (h ->0) ( f(x+h)-f(x) ) /h

and on the right we have
Limit (h -> 0) (f(x+h)-f(x-h))/(2h)

The following animations show a continuous function with discontinuous derivative at x=4.
Animation of a derivative which does not exist

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