Does this derivative have a name?

Question

What is this derivative called: $$ D_\gamma f = \lim_{dt\to 0} \frac{f(\gamma(dt))-f(\gamma(0))}{||\gamma(dt)-\gamma(0)||} $$ It is not the same as the directional derivative or the Gateux derivative on wikipedia. Perhaps it is not as general since it uses a vector norm. (or perhaps it is but I don't see it)

Answer 1

In the case that $\gamma$ is differentiable at $0$, this is very similar to the definition of the Hadamard derivative. There, the existence of $$\frac{f(\bar x + t_n \, h_n) - f(\bar x)}{t_n}$$ is required for all sequences $t_n \searrow 0$ and $h_n \to h$, see https://en.wikipedia.org/wiki/Hadamard_derivative.