Here is the definition of directional derivative given;
$$\lim_{\vec{c} \to \vec{u}} \frac{f(\vec{c} + h\vec{u}) - f(\vec{c})}{h}$$
which gives for a scalar field $f: R^n \to R$, the derivative we get by moving from $\vec{c}$ in the direction of unit vector $\vec{u}$.
But when computing these things, we get different results if we don't use a unit direction. I don't get this part, why is this the case. Isn't $h$ shows the amount we move in the direction $\vec{u}$? So if we give a nonunit vector but same direction, since h goes to $0$, shouldn't we get the same result. After all, we are still moving very very small in the same direction, as long as $h \to 0$.