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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 display="inline">\frac{\Delta y}{\Delta x}</math>. The derivative is then defined as the standard part of the ratio:
:<math>\frac{dy}{dx}=\operatorname{st}\left( \frac{\Delta y}{\Delta x}
===Integral===
Given a function <math>f</math> on <math>[a,b]</math>, one defines the integral <math display="inline">\int_a^b f(x)\,dx</math> as the standard part of an infinite Riemann sum <math>S(f,a,b,\Delta x)</math> when the value of <math>\Delta x</math> is taken to be infinitesimal, exploiting a [[hyperfinite set|hyperfinite]] partition of the interval [''a'',''b''].
===Limit===
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