Examples of the Processes of the Differential and Integral CalculusJ and J. J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 31
Сторінка 4
... logarithmic differential of the function . ( 31 ) Let u = ( a + x ) TM ( b + x ) " , ( 32 ) ( 33 ) log u = m log ( a + x ) + n log ( b + x ) , 1 du u dx du d.x = = m a + x n + b + x ' m n + b + x ( a + x ) " ( b + x ) a + x - - C ...
... logarithmic differential of the function . ( 31 ) Let u = ( a + x ) TM ( b + x ) " , ( 32 ) ( 33 ) log u = m log ( a + x ) + n log ( b + x ) , 1 du u dx du d.x = = m a + x n + b + x ' m n + b + x ( a + x ) " ( b + x ) a + x - - C ...
Сторінка 6
... = ( cos y ) sin y 1 - x ( cos y ) 3 ( +7 ) Let tan- ( ) : 2 1 + taking the logarithmic differential we find dy dx sin y 1 = = - = 1 -Xx 1 + e " , ( 1 − x2 ) } * ( 48 ) If y dy dx = 1 хе 2 - y ( 49 ) Let x ( 1+ y ) § 6 DIFFERENTIATION .
... = ( cos y ) sin y 1 - x ( cos y ) 3 ( +7 ) Let tan- ( ) : 2 1 + taking the logarithmic differential we find dy dx sin y 1 = = - = 1 -Xx 1 + e " , ( 1 − x2 ) } * ( 48 ) If y dy dx = 1 хе 2 - y ( 49 ) Let x ( 1+ y ) § 6 DIFFERENTIATION .
Сторінка 44
... logarithmic differential and eliminating , dy dx x - 2y + y = 0 . ( 8 ) Eliminate a and ẞ from the equation Differentiating , ( x − a ) 2 + ( y − ß ) 2 = r2 . - ( x − a ) + ( y − ß ) dy . - Differentiating again , 1+ - 2 - dy B ...
... logarithmic differential and eliminating , dy dx x - 2y + y = 0 . ( 8 ) Eliminate a and ẞ from the equation Differentiating , ( x − a ) 2 + ( y − ß ) 2 = r2 . - ( x − a ) + ( y − ß ) dy . - Differentiating again , 1+ - 2 - dy B ...
Сторінка 46
... logarithmic differential we have dy da m = 2 - xy n a2 + x2 ( 13 ) Eliminate the functions from y = sin ( log x ) ; the result is x02 d2 y from dy + y = 0 . + Ꮖ dx2 dx ( 14 ) Eliminate the exponential and circular functions mx y = ae ...
... logarithmic differential we have dy da m = 2 - xy n a2 + x2 ( 13 ) Eliminate the functions from y = sin ( log x ) ; the result is x02 d2 y from dy + y = 0 . + Ꮖ dx2 dx ( 14 ) Eliminate the exponential and circular functions mx y = ae ...
Сторінка 71
... ( 4 ) Let u = ( α + α1 x + αz x2 + & c . + α , x " + & c . ) " . Assume this to be equal to A。 + A1∞ + Ag∞2 + & c . + An∞ " + & c . and take the logarithmic differentials of both expressions : equating DEVELOPMENT OF FUNCTIONS . 71.
... ( 4 ) Let u = ( α + α1 x + αz x2 + & c . + α , x " + & c . ) " . Assume this to be equal to A。 + A1∞ + Ag∞2 + & c . + An∞ " + & c . and take the logarithmic differentials of both expressions : equating DEVELOPMENT OF FUNCTIONS . 71.
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