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The video uses $h*v$ because the directional derivative is defined as an infinitesimal rate of change. Using the full vector v would represent a finite step, whereas scaling it by a small scalar h and taking the limit as h approaches 0 captures the instantaneous slope in that direction.

Conditions: The function is differentiable at the point.; The direction is specified by a vector v.; h is a scalar approaching 0.

The video uses $h*v$ because the directional derivative is defined as an infinitesimal rate of change. Using the full vector v would represent a finite step, whereas scaling it by a small scalar h and taking the limit as h approaches 0 captures the instantaneous slope in that direction.

Conditions: The function is differentiable at the point.; The direction is specified by a vector v.; h is a scalar approaching 0.