DIFFERENTIAL AND INTEGRAL CALCULUS. 

 . mk 



Q| V"| , 



A?/ 2 . / mh\ 



- = - m , sin mo; + ; 

 Ax mh \ 2 / ' 



2 



therefore ~ = m 



dx 



(6) y 



sinmh 

 Ay = tan w (x 4 h) tan ma? = 



cosmx cosm (a; + h) ^ 



A?/ 

 ^. 



. _ . . 



Ax mh cosmx cos(mx + mk) ' 



re 



(7) 



therefore -~ = = = m Bec*mx or =m(l+ tan' 2 

 dx COB mx 



7N 

 = cot ?72 [x + n} cotmx = -. 



sinm (x 4- h) sin ma? 1 



Ay sinmh 1 



Aa? mh ' sin mx sin (ma? + mh) ' 



dv m . 



or -^ = -^-5 or -m (1 4 cot ma?). 



(8) ?/ = secm#., 



Aj/ = secTTi (aj + h) secmx 



, mh . ( mh\ 

 2 sin sin [ mx + - ) 



1 t \ i ) 



cosm(x + h) cosma; cos mx cos m (x -f 

 A?/ 



u 



. mh . ( mh\ 



sm - &n[mx + ~] 



2 \ 2 J 



mh cosma? cosm (a? + h) J 



1. 



<?y m sin ma; 



or ~- = -, = m secma? tanma?. 



ax 'cos mx 



The inverse trigonometrical functions may be diffe- 

 rentiated by means of the results found for the direct ones ; 

 but to avoid the ambiguity it is advisable to lay down 



C 



