Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 29
Сторінка 4
... logarithmic differential of the function . ( 31 ) Let u = ( a + x ) " ( b + x ) " , log u = m log ( a + x ) + n log ( b + x ) , 1 du m = u dx a + x du dx n b + x " = ( a + x ) " ( b + x ) " m n + x ) " ( ~ 77 . + a + x b + x ( 32 ) ( 33 ) ...
... logarithmic differential of the function . ( 31 ) Let u = ( a + x ) " ( b + x ) " , log u = m log ( a + x ) + n log ( b + x ) , 1 du m = u dx a + x du dx n b + x " = ( a + x ) " ( b + x ) " m n + x ) " ( ~ 77 . + a + x b + x ( 32 ) ( 33 ) ...
Сторінка 6
... logarithmic differential we find dy dx sin y 1 1 002 ( 1 - x2 ) ( 48 ) If y = 1 + xε3 , dy dx = V - 1 - 2 - y ( 49 ) Let x ( 1 + y ) 3 + y ( 1 + x ) § = 0 ; dy then dx = y y + 2 ( 1 + x ) 3 ( 1 + y ) 3 x • x + 2 ( 1 + x ) 3 ( 1 + y ) 3 ...
... logarithmic differential we find dy dx sin y 1 1 002 ( 1 - x2 ) ( 48 ) If y = 1 + xε3 , dy dx = V - 1 - 2 - y ( 49 ) Let x ( 1 + y ) 3 + y ( 1 + x ) § = 0 ; dy then dx = y y + 2 ( 1 + x ) 3 ( 1 + y ) 3 x • x + 2 ( 1 + x ) 3 ( 1 + y ) 3 ...
Сторінка 44
... logarithmic differential and eliminating , dy dx x - 2y + y = 0 . ( 8 ) Eliminate a and ẞ from the equation ( x − a ) 2 + ( y - ß ) 2 = r2 . - Differentiating , ( x − a ) + ( y − ẞ ) dy - = 0 . dx 2 Differentiating again , 1+ ( dy ) ...
... logarithmic differential and eliminating , dy dx x - 2y + y = 0 . ( 8 ) Eliminate a and ẞ from the equation ( x − a ) 2 + ( y - ß ) 2 = r2 . - Differentiating , ( x − a ) + ( y − ẞ ) dy - = 0 . dx 2 Differentiating again , 1+ ( dy ) ...
Сторінка 46
... logarithmic differential we have dy m xy da = 2 - n a2 + x2 ( 13 ) Eliminate the functions from y = sin ( log x ) ; d'y dy the result is x2 + x da + y = 0 . dx from ( 14 ) Eliminate the exponential and circular functions y = aema sin nx ...
... logarithmic differential we have dy m xy da = 2 - n a2 + x2 ( 13 ) Eliminate the functions from y = sin ( log x ) ; d'y dy the result is x2 + x da + y = 0 . dx from ( 14 ) Eliminate the exponential and circular functions y = aema sin nx ...
Сторінка 71
... 3.4 1.2.3.4.5 + Let u = ( a + α1x + α2 x2 + & c . + an∞ " + & c . ) " . Assume this to be equal to A + A1x + А2x2 + & c . + A „ ¿ ” + & c . and take the logarithmic differentials of both expressions : equating DEVELOPMENT OF FUNCTIONS .
... 3.4 1.2.3.4.5 + Let u = ( a + α1x + α2 x2 + & c . + an∞ " + & c . ) " . Assume this to be equal to A + A1x + А2x2 + & c . + A „ ¿ ” + & c . and take the logarithmic differentials of both expressions : equating DEVELOPMENT OF FUNCTIONS .
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