 | Charles Davies - 1836 - 296 pàgines
...obtain v j. du udv at = 5vv* or by reducing to a common denominator , _ \>du — udv M= ~r— .' hence, the differential of a fraction is equal to the denominator...denominator, divided by the square of the denominator. mm 31 . If the numerator u is constant in the fraction t = — , v its differential will be 0 (Art.... | |
 | Charles Davies - 1838 - 298 pàgines
...we obtain v dt = 5, du udv vv or by reducing to a common denominator ,. vdu — udv * = p .' hence, the differential of a fraction is equal to the denominator...denominator, divided by the square of the denominator. 31. If the numerator u is constant in the fraction t = —, * 1J its differential will be 0 (Art. 22),... | |
 | Albert Ensign Church - 1842 - 330 pàgines
..., or <is sdv du = 3 ; V )T whence by reducing to a common denominator _j* _v^s — *^u /i\ that is, the differential of a fraction is equal to, the denominator...denominator, divided by the square of the denominator. If the denominator be constant, dv = o, and equation (1) becomes vds ds du — —5- = — . VV If... | |
 | Elias Loomis - 1851 - 300 pàgines
...Ans. Ex. 5. What is the differential of ax\xl+a) (x+3b) 1 Ans. PROPOSITION XI. — THEOREM. (184.) The differential of a fraction is equal to the denominator...denominator, divided by the square of the denominator. Let us designate the fraction by -, and suppose 1=9, (0 u=vy. 1 ' Therefore, by Prop. IX., du=ydv+vdy... | |
 | Albert Ensign Church - 1855 - 368 pàgines
...du = --- r; v tr whence by reducing to a common denominator , , A vds — sdv ,.. ч (1), that is, the differential of a fraction is equal to, the denominator into the differential of thc numerator, minus tJ»e numerator into the differential of the denominator, divided by the square... | |
 | Elias Loomis - 1859 - 320 pàgines
...Ans. Ex. 5. What is the differential of ax'(x'+a) (x+3b) ? Ans. v PROPOSITION XI. — THEOREM. (184.) The differential of a fraction is equal to the denominator...denominator, divided by the square of the denominator. Let us designate the fraction by -, and suppose 5-* ' W then u=vy. Therefore, by Prop. IX., du—ydv+vdy... | |
 | Albert Ensign Church - 1864 - 410 pàgines
...dl tdv du = --- - ; v v' whence, by reducing to a common denominator, * vds — sdv v (1); that is, the differential of a fraction is equal to the denominator...differential of the numerator, minus the numerator into tht differential of the denominator, divided by the square of the denominator. If the denominator be... | |
 | Albert Ensign Church - 1870 - 392 pàgines
...= j-; VV* whence, by reducing to a common denominator, vds — »dv du - d- = v •0); that is, tho differential of a fraction is equal to the denominator...denominator, divided by the square of the denominator. If the denominator be constant, dv = 0, and equation (1) become« or If the numerator be constant,... | |
 | Edward Olney - 1871 - 394 pàgines
...constant numerator and a variaUe denominator is the product of the numerator with ifa s:gn changed into the differential of the denominator, divided by the square of the denominator. SCH.— If the numerator is variable and the denominator constant it falls tinder Rule 2. 56. RULE... | |
 | Edward Olney - 1873 - 354 pàgines
...constant numerator and a variable denominator is the product of the numerator with its sign changed into the differential of the denominator, divided by the square of the denominator. Let и = — . Differentiating this by the rule and calling the differential of ¿f 4.1 4. i \ л ij... | |
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V )T whence by reducing to a common denominator _j* _v^s — *^u /i\ that is, the differential of a fraction is equal to, the denominator into the differential of the numerator, minus the numerator into the differential of the denominator, divided by... 
