# Directional derivative

The limit (if it exists) of the rate of change along a specified direction, say $LaTeX: h$,
$LaTeX: \lim_{t \rightarrow 0^+} \frac{f(x+th) - f(x)}{t}$.
In particular, the $LaTeX: i$-th partial derivative is with $LaTeX: h=e_i$. (Note that the directional derivative, as defined above, depends on the scale: the derivative for $LaTeX: kh$ is $LaTeX: k$ times the derivative for $LaTeX: h$. To avoid scale dependence, some authors require $LaTeX: \|h\| = 1$.) Recently, some people have called this a B-derivative (or Bouligand derivative), and functions that have directional derivatives in all feasible directions are B-differentiable. Some require the convergence to be uniform.