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derivative
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Definition/Summary
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The derivative of a function [itex]y=f(x)[/itex] is the rate of change of [itex]y[/itex] per change in [itex]x[/itex]. It is denoted by [itex]\frac{\mathrm dy}{\mathrm dx}[/itex]. Let [itex]\Delta x[/itex] be a change in [itex]x[/itex], and [itex]\Delta y[/itex] be the corresponding change in [itex]y[/itex] caused by the change in [itex]x[/itex]. The derivative, in standard calculus, is defined as
[tex]\lim_{\Delta x\rightarrow 0}\frac{\Delta y}{\Delta x}.[/tex]
In nonstandard calculus, it is defined as
[tex]\mbox{st}\left(\frac{\Delta y}{\Delta x}\right),[/tex]
where st denotes the standard part function and [itex]\Delta x[/itex] is infinitesimal. |
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Recent forum threads on derivative
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Breakdown
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Mathematics
> Calculus/Analysis
>> Calculus
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Commentary
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