 | Charles Davies - 1836 - 296 σελίδες
...the differential coefficients of y, z, and w, regarded as functions of x, it follows (Art. 17) that, the differential of the sum, or difference of any...difference of their differentials taken separately. 28. Let us now determine the differential of the product of two variable functions. If we designate... | |
 | Charles Davies - 1838 - 300 σελίδες
...the differential coefficients of y, z, and w, regarded as functions of x, it follows (Art. 17) that, the differential of the sum, or difference of any...difference of their differentials taken separately. 28. Let us now determine the differential of the product of two variable functions. If we designate... | |
 | Charles Davies - 1838 - 298 σελίδες
...the differential coefficients cf y, z, and 10, regarded as functions of x, it follows (Art. 17) that, the differential of the sum, or difference of any...same variable, is equal to the sum or difference of theii- differentials taken •separately. % 28. Let us now determine the differential of the product... | |
 | Charles Davies - 1840 - 302 σελίδες
...functions of x, it follows (Art. 17) that, the differential of the sum, or difference of any member of functions, dependent on the same variable, is equal...difference of their differentials taken separately. 28. Let us now determine the differential of the product of two variable functions. If we designate... | |
 | Albert Ensign Church - 1842 - 330 σελίδες
...dv it rfw ± dz, that is ; <Ae differential of the sum or difference of any number of functions of the same variable is equal to the sum or difference of their differentials taken separately. Thus, if « — ax1 — ba? du = d(ax*) - d(6a^) = 2axdx - 3ba?dx ............ Arts. (7 & 9). 19. Let... | |
 | Albert Ensign Church - 1842 - 340 σελίδες
...; or since, Qdz = dv, Rdx = die, Sdж = dz ............ Art. (8), du — d« ± dw ± dz, that is ; the differential of the sum or difference of any number of functions of the same variable is equal to the sum or difference of their differentials taken separately. Thus,... | |
 | Elias Loomis - 1851 - 296 σελίδες
...This new value of the function will be frequently referred to hereafter under the form u'=u+Ah+Eh'. (2) PROPOSITION VIII. — THEOREM. (179.) The differential...example, u=y+z— v, where y, z, and v are functions of a;. If we change x into x+h, we shall have u'—u=(y'—y) + (z'—z) — (v'—v). But by the preceding... | |
 | Elias Loomis - 1851 - 300 σελίδες
...be frequently referred to hereafter under the form K'=w+AA+BA'. (2) PHOPOSITION VIII. — THEOREM. i (179.) The differential of the sum or difference of...terms, as, for example, u=y+z— v, where y, z, and u are functions of x. If we change x into x+h, we shall have But by the preceding Proposition y'—y... | |
 | Elias Loomis - 1856 - 300 σελίδες
...This new value of the function will be frequently referred to hereafter under the form «'=tt+AA+BA'. (2) PROPOSITION VIII. — THEOREM. (179.) The differential...But by the preceding Proposition y'—y may be put unoe the form of AA+BA3. So, also, z'—z may be put under the form of A'A+B'A : and v'—v may be... | |
 | Albert Ensign Church - 1870 - 392 σελίδες
...± dw ± dz; that is, <Лe differential of tfic sum or difference of aay number of functions of liie same variable, is equal to the sum or difference of their differentials taken separately. Thus, if u = ax' — bx*, du = d (аz') — d (bx*) — Zaxdx — SЬхЧх. . .Arts. (9 & 11). 21.... | |
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This new value of the function will be frequently referred to hereafter under the form «'=tt+AA+BA'. (2) PROPOSITION VIII. — THEOREM. (179.) The differential of the sum or difference of any number of functions dependent on the same variable, is equal... 
