EXAMPLES VI 97 



dy 



and T- 



(1 - * 



tin 

 , V-: 



/IA TT ^ i V * 



(6) Using the rule -/ - 5 



dx v- 



. du 



u = 1 + x 2 and -j- = 2* 

 cfcc 



,. J , dv I 



t> = (1 - x 2 ) * and - - 



dx 2 Vl - a; 2 Vl - x 2 



T ' r L 



cte 1 



= j {2x(l - x 2 ) + x(l + x z ) } 



(1 - x*f 



(l-a? 2 )' 



In general the most straightforward method to use for dif- 

 ferentiation is to work logarithmically, and this should be used 

 in all cases where it is possible. 



EXAMPLES VI 

 Differentiate with respect to x. 



(1) e slna> (2) eV* 



(3) \og e sin x (4) x sin x 



(5) SIL*. (6) -4- 



x v ' sin x 



(7) a? sin a; (8) 



(9) a; n log e x (10) x* log a x 



(11) a: 4 tan a; (12) x n log, sin a; 



(13) -J-- (14) 



(15) 



sm m; a;" 



e 

 sin w# 



(17) "* cos nx (18) *r w 6" sin nx 



(19) g^ tan nx (20) e"* sec na? 



G 



