In mathematics, is about the way a function changes, in particular the (first) differential of a simple function of one variable is its slope. For a simple function this is a single number representing the rate of growth (or decline) of the function. For a function of more than one variable, say the height of terrain on a map, the (first) differential is a vector erepresenting the size and direction of maximum ascent. The second deifferential is the rate of change of the first differential; for example, velocity is the rate of change of location (first differential) and accelaration is the rate of change of velocity (second differential). Higher differentials are used also, for exampel, in planning train lines engineers consider 'jerk', the rate of change of acceleration, which is a third differential.
Used on pages 116, 188, 253