l6o MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



7.368 



+ C^P(P -I)(P- 2) (log X)V~* - . . . J, 



where p is a positive integer. If n<p there are n terms in the series. If 



2. -(k>g *)* = - Cn-lXlOg X)P~1 - Cn-2p(P ~ I) (log *)- 2 



U'.V .V ^ 



+ ..... + (-l) P+1 C n . p p(p- l)(p- 2) .... 2-1 



( } P P P+i x p+l p+2 



7.369 (log ( I + ,)} =C eX >-C l + C 2 



- I < X < + I. 



7.37 Derivatives of Powers of Functions. If y = <f>(x). 

 n - p . 



T 



fn\ i 



7.38 



! ^^^n^ = ( ~ ^( m ~ 2 ) ...... (w - [ - i]) 



d n (a + bx)~ l , nlb n 



dx n l) (a+.be)**? 



d n (a + bx) 

 



J" log (a + fty) _ r . _, ( 

 } 



_ 

 dx n (a 



IX 



= a n e ax . 



, n sn x 



d n cos ^ 



7- T~ = COS 



