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
... dy 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 ds dy = dx da dv ds dy Ex . ( 1 ) Let u = ( a + bx " ) " . Then y = a + bx " , u = y TM ...
... dy 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 ds dy = dx da dv ds dy Ex . ( 1 ) Let u = ( a + bx " ) " . Then y = a + bx " , u = y TM ...
Сторінка 6
... dy then - ( - ) dx = log y -y log If sin ya sin ( a + y ) , dy da = sin ( a + y ) cos y x cos ( a + y ) If y " log y = ax , dy dx ( 46 ) If tan y = dy dx ( 47 ) Let tan = y 2 = -1 a y - 1 ( 1 + nlogy ) 1 + x sin y , ( cos y ) 2 sin y ...
... dy then - ( - ) dx = log y -y log If sin ya sin ( a + y ) , dy da = sin ( a + y ) cos y x cos ( a + y ) If y " log y = ax , dy dx ( 46 ) If tan y = dy dx ( 47 ) Let tan = y 2 = -1 a y - 1 ( 1 + nlogy ) 1 + x sin y , ( cos y ) 2 sin y ...
Сторінка 7
... dy { a2 − 2 ( x2 + y2 ) } x dx { b2 + 2 ( x2 + y2 ) } y ' = - ( 52 ) Let ( a + y ) 2 ( b2 — y2 ) — x2 y2 then dy dx = y2 ( b * — y3 ) } y3 + ab2 = 0 , Functions of Two or more Variables . ( 53 ) u = ( - ) ( 54 ) du dx = du = u = du ...
... dy { a2 − 2 ( x2 + y2 ) } x dx { b2 + 2 ( x2 + y2 ) } y ' = - ( 52 ) Let ( a + y ) 2 ( b2 — y2 ) — x2 y2 then dy dx = y2 ( b * — y3 ) } y3 + ab2 = 0 , Functions of Two or more Variables . ( 53 ) u = ( - ) ( 54 ) du dx = du = u = du ...
Сторінка 22
... dy'dx drs u = dx'dy s = 1 , u = xy " ; r = 1 , du dx mxm - 1y " ; = d2 u dy da = m n xm m - 1 1y " - 1 du dy = = n - 1 nx " yr- d'u dx dy ( 2 ) W = x2 + y2 x2 du dy dx = - 1 ' = 1 , s = 1 , y2 8xy a2 + y2 ( x2 - y2 ) " r = 1 , 8 = 1 , ď u 1 ...
... dy'dx drs u = dx'dy s = 1 , u = xy " ; r = 1 , du dx mxm - 1y " ; = d2 u dy da = m n xm m - 1 1y " - 1 du dy = = n - 1 nx " yr- d'u dx dy ( 2 ) W = x2 + y2 x2 du dy dx = - 1 ' = 1 , s = 1 , y2 8xy a2 + y2 ( x2 - y2 ) " r = 1 , 8 = 1 , ď u 1 ...
Сторінка 23
... is indifferent . x02 du dx - 2x2yz ( a2 — x2 ) 3 3 ( 10 ) u = x2y a2 - du dx a2 d2 u dx dy d2 u dx dx = = 2xy a2 - 2x - ~ 2 = 4xyx ( a2 - 3 ) 2 du dy d2 u dyd x = a2 du 9 dx dx - > d'u dyd d3 u dx dy dz = == = SUCCESSIVE DIFFERENTIATION .
... is indifferent . x02 du dx - 2x2yz ( a2 — x2 ) 3 3 ( 10 ) u = x2y a2 - du dx a2 d2 u dx dy d2 u dx dx = = 2xy a2 - 2x - ~ 2 = 4xyx ( a2 - 3 ) 2 du dy d2 u dyd x = a2 du 9 dx dx - > d'u dyd d3 u dx dy dz = == = SUCCESSIVE DIFFERENTIATION .
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