then 



PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 

 ^jf-^ = \ogx . .(-1)" + ^ -^~ . -(log^-Q.„) 



593 



+ ^.(_l)n.^^._i_(l0g._Q,^,) 



_ n(n-l) _1_ f_,y^j /n-2 _J 

 1.2 ' X? ^ ' j-\ ' «»■ 



+ &c. 



•(Iog«-Q„_2) 





+ (-1)' 



/^ 



/w^ 1.2 w(w-l)(w-2) 



/-I «" 



12.3 (l'>g*^-Q.^-3) 



+ &c. 



= -(_l)n.._^.iy-.(l0g^-Q„) 



. (-1 )»^ 4 • ( » (log.-Q^o + -5^f^ aog.-a._.) 



W(» — 1)(«-2) in,, „ , „ 1 



•" l.2.3(.-2)(.-3) l-2(log^-Q„-a) + &c. } 



/ n , n(n-\ ) 1 »(»-l)(»-2) 1 ^ \ , 



- r'^-^-^TiT-- 2*^-+ib2)it3r • ¥^- + ■••)} 



Section III. — Circular Functions. 

 22. To find the differential Goeffident ofcosmx to any index n. 

 Since cos mx=— {f" ^-^ + e-™^ '^^) 



' cos »8 a 1 „ f , , , „ , j~r , /— - 



'dH^ "¥ I (\/-l)"e"'"^-' +(_v'-l)"e-''-^'-i 



/ 



