Standard part function: Difference between revisions

Revision as of 16:14, 5 February 2014

Revision as of 20:37, 28 October 2014

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:<math>f'(x) = \operatorname{st}\left(\frac {f(x+h)-f(x)}h\right).</math>

Alternatively, if <math>y=f(x)</math>, one takes an infinitesimal increment <math>\Delta x</math>, and computes the corresponding <math>\Delta y=f(x+\Delta x)-f(x)</math>. One forms the ratio <math>\frac{\Delta y}{\Delta x}</math>. The derivative is then defined as the standard part of the ratio:

:<math>\frac{dy}{dx}=\textmathrm{st}\left( \frac{\Delta y}{\Delta x} \right)</math>.

==See also==