What is "partial differentiation"

partial \par"tial\ (p[aum]r"shal), a. [F., fr. LL. partials, fr. L. pars, gen. partis, a part; cf. (for sense 1) F. partiel. See Part, n.]

1. Of, pertaining to, or affecting, a part only; not general or universal; not total or entire; as, a partial eclipse of the moon. ``Partial dissolutions of the earth.''
   --T. Burnet.

2. Inclined to favor one party in a cause, or one side of a question, more then the other; biased; not indifferent; as, a judge should not be partial.

   Ye have been partial in the law.
   --Mal. ii. 9.

3. Having a predilection for; inclined to favor unreasonably; foolishly fond. ``A partial parent.''
   --Pope.

   Not partial to an ostentatious display.
   --Sir W. Scott.

4. (Bot.) Pertaining to a subordinate portion; as, a compound umbel is made up of a several partial umbels; a leaflet is often supported by a partial petiole.

   Partial differentials, Partial differential coefficients, Partial differentiation, etc. (of a function of two or more variables), the differentials, differential coefficients, differentiation etc., of the function, upon the hypothesis that some of the variables are for the time constant.

   Partial fractions (Alg.), fractions whose sum equals a given fraction.

   Partial tones (Music), the simple tones which in combination form an ordinary tone; the overtones, or harmonics, which, blending with a fundamental tone, cause its special quality of sound, or timbre, or tone color. See, also, Tone.