Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 100
Сторінка 1
... dx dy dx y being some function of x , and u some function of y . This theorem may be extended to any number of functions , so that du du dv dz dy = do dv dx dy dx Ex . ( 1 ) Let u = Then y = a + bx " , ( a + bxn ) TM . u = y TM , dy du ...
... dx dy dx y being some function of x , and u some function of y . This theorem may be extended to any number of functions , so that du du dv dz dy = do dv dx dy dx Ex . ( 1 ) Let u = Then y = a + bx " , ( a + bxn ) TM . u = y TM , dy du ...
Сторінка 6
... dy dx y ( y x log y = - 00 - - If sin y = x sin ( a + y ) , dy dx = y log x sin ( a + y ) cos y x cos ( a + y ) ( 45 ) If y " log y = ax , dy = - a dx y " -1 ( 1 + nlogy ) ( 46 ) If tan y = 1 + x sin y , dy ( cos y ) 2 sin y dx = 1 - x ...
... dy dx y ( y x log y = - 00 - - If sin y = x sin ( a + y ) , dy dx = y log x sin ( a + y ) cos y x cos ( a + y ) ( 45 ) If y " log y = ax , dy = - a dx y " -1 ( 1 + nlogy ) ( 46 ) If tan y = 1 + x sin y , dy ( cos y ) 2 sin y dx = 1 - x ...
Сторінка 7
... dy dx : = { a2 - 2 ( x2 + y3 ) } x { b2 + 2 ( x2 + y2 ) } y ( 52 ) Let ( a + y ) 2 ( b2 — y2 ) — x2 y2 = 0 , then - dy y2 ( b2 — y2 ) } dx = - y3 + aba Functions of Two or more Variables . √ ( 39 ) - ( - ) ( 54 ) W = du = , 2xy2 du ...
... dy dx : = { a2 - 2 ( x2 + y3 ) } x { b2 + 2 ( x2 + y2 ) } y ( 52 ) Let ( a + y ) 2 ( b2 — y2 ) — x2 y2 = 0 , then - dy y2 ( b2 — y2 ) } dx = - y3 + aba Functions of Two or more Variables . √ ( 39 ) - ( - ) ( 54 ) W = du = , 2xy2 du ...
Сторінка 22
... dy ' da u = xm yn ; r = 1 , dr + su = da'dy 8 = 1 , du du = mxm − 1y " ; dx du dy da ' yn - 1 -1 dy = = nx " y " -1 ; du dx dy ( 2 ) u = = m n xm - 1 ? x2 + y2 x2 d2 u dy dx - - y2 ; r = 1 , 8xy x2 + y2 ( x2 - y2 ) 3 8 = 1 , ď2 u = dx dy ...
... dy ' da u = xm yn ; r = 1 , dr + su = da'dy 8 = 1 , du du = mxm − 1y " ; dx du dy da ' yn - 1 -1 dy = = nx " y " -1 ; du dx dy ( 2 ) u = = m n xm - 1 ? x2 + y2 x2 d2 u dy dx - - y2 ; r = 1 , 8xy x2 + y2 ( x2 - y2 ) 3 8 = 1 , ď2 u = dx dy ...
Сторінка 23
... dx y y r = 1 , 8 = 1 ; ( y2 — x2 ) } - = d2 u dx dy du u = tan - 1 = 30 y x2 - y2 ; dy dx ( y2 + x2 ) 2 r = 1 , 8 = 1 ; du = dx dy u = x sin y + y sin x ; r = 1 , s = 1 ; ( 8 ) d2 u du = cos y + cos x = dy dx da dy ( 9 ) u = sin x cos y ; r ...
... dx y y r = 1 , 8 = 1 ; ( y2 — x2 ) } - = d2 u dx dy du u = tan - 1 = 30 y x2 - y2 ; dy dx ( y2 + x2 ) 2 r = 1 , 8 = 1 ; du = dx dy u = x sin y + y sin x ; r = 1 , s = 1 ; ( 8 ) d2 u du = cos y + cos x = dy dx da dy ( 9 ) u = sin x cos y ; r ...
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