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" COR. — The differential of a fraction having a 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... "
A University Algebra: Comprising a Compendious, Yet Complete and Thorough ... - Page 158
by Edward Olney - 1882 - 323 pages
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Elements of the Differential and Integral Calculus

Charles Davies - Calculus - 1836 - 296 pages
...a fraction is equal to the denominator into the differential of the numerator, minus the numerator into the differential of the 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....
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Elements of the Differential and Integral Calculus

Charles Davies - Calculus - 1838 - 300 pages
...a fraction is equal to the denominator into the differential of the numerator, minus the numerator into the differential of the denominator, divided by the square of the denominator. 31 . If the numerator u is constant in the fraction t = — , v its differential will be 0 (Art. 22),...
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Elements of the Differential and Integral Calculus

Albert Ensign Church - Calculus - 1842 - 330 pages
...a fraction is equal to, the denominator into the differential of the numerator, minus the numerator into the differential of the 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...
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Elements of Analytical Geometry and of the Differential and Integral Calculus

Elias Loomis - Calculus - 1851 - 300 pages
...a fraction is equal to the denominator into the differential of the numerator, minus the numerator into the differential of the 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 ;...
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Elements of Analytical Geometry and of the Differential and Integral Calculus

Elias Loomis - Calculus - 1851 - 296 pages
...a fraction is equal to the denominator into the differential of the numerator, minus the numerator into the differential of the denominator, divided by the square of the denominator. u Let us designate the fraction by -, and suppose then u=vy. Therefore, by Prop. IX., du=ydv+vdy ;...
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Elements of Analytic Geometry and of the Differential and Integral Calculus

Elias Loomis - Calculus - 1859 - 320 pages
...a fraction is equal to the denominator into the differential of the numerator, minus the numerator into the differential of the 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...
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A General Geometry and Calculus: Including Book I. of the General Geometry ...

Edward Olney - Calculus - 1871 - 396 pages
...— -. <JED 53, COR. — The differential of a fraction having a constant numerator and a variafjle denominator is the product of the numerator with its...denominator, divided by the square of the denominator. DEM. — Let u = -. Differentiating this by the rule and calling the differential , , , , 0 — ttfhi...
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A General Geometry and Calculus: Including Part I. of the General Geometry ...

Edward Olney - Calculus - 1871 - 402 pages
...value, we have .' — : — \- ydu = dx. Finding the value of du, we have du = ^—^ -. y yQED 55. COR. — The differential of a fraction having a constant numerator and a variable denominator in the product of the numerator with its sign changed into the differential of the denominator, divided...
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A General Geometry and Calculus: Including Part I. of the General Geometry ...

Edward Olney - Calculus - 1871 - 394 pages
...its value, we have ' — : — f- ydu = dx. Finding the value of du, we have du = ^— -— . QED 55. COR. — The differential of a fraction having a constant numerator and a variaUe denominator is the product of the numerator with ifa s:gn changed into the differential of...
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A University Algebra ...

Edward Olney - Algebra - 1873 - 354 pages
...+ ydu = dx. Finding the value of if У , -, : ydx — xdy du, we have du — - - ¿ — -. QED У . COR. — The differential of a fraction having a constant...Differentiating this by the rule and calling the differential of ¿f 4.1 4. i \ л ij 0 — ady — ndy the constant (a) 0, we nave du = - - ¿ — — = - 1-= . QED...
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