PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 593 



then _£lfe^ ^ I , (_!)„,, ^ _ 1 (log.-Q„) 



- 1.2 • -^ (-1) T^T • 1^ (^^s^-Q"-2) 



+ &c. 



= (-l)-.-^.i|i(log.-Q,.) 



/—I ^ 





+ &c. 



= (_!)».! ^.J^. (log :._Q„) 



■*■ 1.2.3(^-2) (.-3) l-2(log^-Q„-3) + &c. I 



= (-i)"^^7^^(iog-<^.) 



/ n , w(w-l ) 1^ , nin-X^in-"^ 1 ^ v ^ 



- (»'^-' + -^::2- • 2 '^-'-^- (.-2) (1-3) • 3 Q- + •••) ) 



Section III. — Circular Functions. 

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



_ V— 1 4. ^— m a; V— 1 



2 ^^ 

 (?" cos ma; 1 



Since cosma;=— (e™* '^-i + e-"^ >'-i) 



• 2 



dgf 



■= 2-m«| (^/3l)«e--^^-l +(_Vri)«e-»W-i 1 



