Calculus And Probability for Actuarial Students
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To quickly assess the difficulty of the text, read a short excerpt:
. . , , 1 dy _1 du 1 dv 1 dw y dx udx v dx w dx dy _ ri du 1 dv 1 dw dx \_u dx v dx w dx "' y a result which agrees with that already obtained in § 1. Secondly if y = u v, u and v both being functions of x, \ogy = v log u, , 1 dy v du . Dv and --/=- + W ^ — y a# wo« ° dx dy „, du ml dv or -/ = vu v ~ x -j- + u v log w -T- .
dx dx ° dx 5. We will now give some miscellaneous examples of differen- tiation.
, . * a + x 2 (1) r-5+7- By the ordinary rule for a quotient dx (6 + x)' z ■ (& + a?)2a?-(a ...+ a: 2 ) * x 2 + 26a; - a (b + xf (b + a;) 2 ' , .. * 7a? -1 (U) ^ l-Ss+6^ This can best be treated by resolving the expression into partial fractions. Then 4 5 y l-3a? l-2a?' dy d (1 - 3a?)- 1 d (1 - 3a?) d (1 - 2a?)- 1 d (1 - 2a?) da?" d(l-3a?) * dx d(l-2x)' dx 12 10 (l-3a?) 2 (l-2a?) 2 * STANDARD FORMS 71 (iii) y = \/a + x. . '''....
1 dy d(a + x) n d(a + x) 1, ,--i -/■ = - T 7 t-— S -=-(a + a?) n .
ax d(a + x) dx n \ (iv) y = log (log x).
dy _ d log (log x) d (log #) 1 ofo? rf (log #) cfo?
What to read after Calculus And Probability for Actuarial Students?
You can find similar books in the "Read Also" column, or choose other free books by Alfred Henry to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
. . , , 1 dy _1 du 1 dv 1 dw y dx udx v dx w dx dy _ ri du 1 dv 1 dw dx \_u dx v dx w dx "' y a result which agrees with that already obtained in § 1. Secondly if y = u v, u and v both being functions of x, \ogy = v log u, , 1 dy v du . Dv and --/=- + W ^ — y a# wo« ° dx dy „, du ml dv or -/ = vu v ~ x -j- + u v log w -T- .
dx dx ° dx 5. We will now give some miscellaneous examples of differen- tiation.
, . * a + x 2 (1) r-5+7- By the ordinary rule for a quotient dx (6 + x)' z ■ (& + a?)2a?-(a ...+ a: 2 ) * x 2 + 26a; - a (b + xf (b + a;) 2 ' , .. * 7a? -1 (U) ^ l-Ss+6^ This can best be treated by resolving the expression into partial fractions. Then 4 5 y l-3a? l-2a?' dy d (1 - 3a?)- 1 d (1 - 3a?) d (1 - 2a?)- 1 d (1 - 2a?) da?" d(l-3a?) * dx d(l-2x)' dx 12 10 (l-3a?) 2 (l-2a?) 2 * STANDARD FORMS 71 (iii) y = \/a + x. . '''....
1 dy d(a + x) n d(a + x) 1, ,--i -/■ = - T 7 t-— S -=-(a + a?) n .
ax d(a + x) dx n \ (iv) y = log (log x).
dy _ d log (log x) d (log #) 1 ofo? rf (log #) cfo?
What to read after Calculus And Probability for Actuarial Students?
You can find similar books in the "Read Also" column, or choose other free books by Alfred Henry to read onlineMoreLess
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