differential

adj

1. Of or pertaining to a difference.

   “differential characteristics”

   “I saved disk space by taking differential backups, which only stored the data that had changed.”

   “[Caspar Schetz, Baron of Grobbendonck] was regularly in the pay of Sir Thomas Gresham, to whom he produced differential favours, and by whose government he was rewarded by gold chains and presents of hard cash, bestowed as secretly as the equivalent was conveyed adroitly.”

2. Dependent on, or making a difference; distinctive.
3. Having differences in speed or direction of motion.
4. Of or pertaining to differentiation or the differential calculus.

noun

1. The differential gear in an automobile, etc.
2. A qualitative or quantitative difference between similar or comparable things.
3. One of two coils of conducting wire so related to one another or to a magnet or armature common to both, that one coil produces polar action contrary to that of the other.
4. A form of conductor used for dividing and distributing the current to a series of electric lamps so as to maintain equal action in all.
5. A quantity representing an infinitesimal change in a variable, now only used as a heuristic aid except in nonstandard analysis but considered rigorous until the 20th century; a fluxion in Newtonian calculus, now usually written in Leibniz's notation as operatorname d!x.
6. A function giving the change in the linear approximation of f at a point x over a small interval Δx or operatorname d!x, the function being called the differential of f and denoted operatorname d!f(x,Δx), operatorname d!f(x), or simply operatorname d!f.

   “If f(x)#61;x², the differential of f is the function #92;operatorname#123;d#125;#92;#33;f(x,#92;Deltax)#61;f'(x)#92;Deltax#61;2x#92;Deltax.”

7. A function giving the change in the linear approximation of f at a point x over a small interval Δx or operatorname d!x, the function being called the differential of f and denoted operatorname d!f(x,Δx), operatorname d!f(x), or simply operatorname d!f.
8. The Jacobian matrix of a function of several variables.
9. The pushforward or total derivative of ϕ: a linear map from the tangent space at a point x in ϕ's domain to the tangent space at ϕ(x) which is, in a technical sense, the best linear approximation of ϕ at x; denoted operatorname d!ϕₓ.
10. Any of several generalizations of the concept(s) above: e.g. the Kähler differential in the setting of schemes, the quadratic differential in the theory of Riemann surfaces, etc.