Let’s first look at the concepts of scalar and vector.
Scalars are quantities with only magnitude and no direction, like weight, exam
scores, or height. Vectors, on the other hand, have both magnitude and
direction, like magnetic force, velocity, and acceleration.
Application of Partial
Derivative (Cited from Wikipedia)
The quadratic function f(x) = x2 has pairs
of values (x, y) that are scalars. For instance, (x, y) = (-1, 1) or (x, y) =
(1, 1). Differentiating function f(x) yields f'(x) = 2x, which can be used to
find the rate of change at a particular point. The concept of rate of change
implies direction. At x = -1, the rate of change is -2, indicating a decrease,
while at x = 1, the rate of change is 2, indicating an increase. Scalars, when
differentiated or partially differentiated, become vectors with direction.
