Definition:Differential of Mapping/Real Function

On an Open Set
Also:
 * $f \left({x + h}\right) - f \left({x}\right) - \mathrm d f \left({x; h}\right) = o \left({h}\right)$

as $h \to 0$.

In the above, $o \left({h}\right)$ is interpreted as little-O of $h$.

Also see

 * Straight Line Defined by Differential, where it is shown that for any fixed $x \in \R$, the equation:
 * $k = \mathrm d f \left({x; h}\right) = f' \left({x}\right) h$

is the equation of a straight line, tangent to the graph of the real function $f$ at the point $x$.