Definition:Differential of Mapping/Real Function

On an Open Set
Also:
 * $\map f {x + h} - \map f x - \map {\d f} {x; h} = \map o h$

as $h \to 0$.

In the above, $\map o h$ 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:
 * $k = \map {\d f} {x; h} = \map {f'} x h$

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