Examples of the Processes of the Differential and Integral Calculus |
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Page 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 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 , dy ...
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... dx a log a log2 x ...... log - 1 x du ( 8 ) u = log ( sin x ) ; = cot x . dx $ 1 - Cos m x du m ( 9 ) U = = log ( ; 1+ cos m x dx sin ma du 2 ( 10 ) u = log ( tan r ) , dx sin 2 x du ( 11 ) u = cos ( sin x ) ; = -- cos a sin2 , dx sin ...
... dx a log a log2 x ...... log - 1 x du ( 8 ) u = log ( sin x ) ; = cot x . dx $ 1 - Cos m x du m ( 9 ) U = = log ( ; 1+ cos m x dx sin ma du 2 ( 10 ) u = log ( tan r ) , dx sin 2 x du ( 11 ) u = cos ( sin x ) ; = -- cos a sin2 , dx sin ...
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... dx u = < -1 -1 b2 - 00 a2 a2 a2 ) ( b2 00 - 1 " 2 = 2x ( a1 − x1 ) } - " · x2 ) } } ° du dx x2 ) 3 − = 1 ( 1 + 2 x − x2 ) } * du - - 1 z = tan ~ ' { ( 1 + a1 ) ) — x } , === ( 1+ ) ( 19 ) u = sin- ( 20 ) 2x ( 21 ) dy u = tan - ...
... dx u = < -1 -1 b2 - 00 a2 a2 a2 ) ( b2 00 - 1 " 2 = 2x ( a1 − x1 ) } - " · x2 ) } } ° du dx x2 ) 3 − = 1 ( 1 + 2 x − x2 ) } * du - - 1 z = tan ~ ' { ( 1 + a1 ) ) — x } , === ( 1+ ) ( 19 ) u = sin- ( 20 ) 2x ( 21 ) dy u = tan - ...
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... dx ( 1 + e cos x ) 2 3e + ( 2 + e2 ) cos x ( 1 + e cos x ) 3 du = dx ( 1 − x ) $ - x cos ( a2 — x2 ) { sin ( a2 – x2 ) } du ( 29 ) u = { sin ( a2 - x2 ) } } , dx du = dx ( 1 - ( 30 ) u = log cos - 1 ( 1 – 2 ) , --- 1 x ) sin1x When a ...
... dx ( 1 + e cos x ) 2 3e + ( 2 + e2 ) cos x ( 1 + e cos x ) 3 du = dx ( 1 − x ) $ - x cos ( a2 — x2 ) { sin ( a2 – x2 ) } du ( 29 ) u = { sin ( a2 - x2 ) } } , dx du = dx ( 1 - ( 30 ) u = log cos - 1 ( 1 – 2 ) , --- 1 x ) sin1x When a ...
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... dx ( x + 2 ) 3 ( ( x + 3 ) " ) x + 1 ( 37 ) u = x2 , log u = x log x , du ( 38 ) 6868 ( 39 ) ( 40 ) da = ( 1 + log x ) ... dx = 00 ( sin x ) -1 ( cos x ) " - 1 ( m cos2 x - n sin2 x ) . ( sin x ) TM u = ( cos x ) " du ( sin x ) m - 1 = ( m ...
... dx ( x + 2 ) 3 ( ( x + 3 ) " ) x + 1 ( 37 ) u = x2 , log u = x log x , du ( 38 ) 6868 ( 39 ) ( 40 ) da = ( 1 + log x ) ... dx = 00 ( sin x ) -1 ( cos x ) " - 1 ( m cos2 x - n sin2 x ) . ( sin x ) TM u = ( cos x ) " du ( sin x ) m - 1 = ( m ...
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