Given a function *f*, we have defined its derivative *f'*. This allows us to now define
*f''*, the *second derivative* of *f*, to be the derivative of *f'*. In terms of the
graph of *f*, the second derivative tells how quickly the slope of the graph is changing
near a particular point. Alternately, the second derivative tells how quickly the rate
of change of a function is changing.

Since *f''* is again a function, we can define *f'''* = *f*^{(3)} to be the derivative of
*f''*. Continuing in this way, we can define the *nth* derivative of *f*, *f*^{(n)}.
The derivative of a differentiable function need not be differentiable everywhere
(or even anywhere), so in general the domains of the successive derivatives *f*^{(}*n*)
shrink as *n* increases.

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