48 DIFFERENTIAL COEFFICIENTS. 



It is obvious that other self- verify ing examples may be 

 constructed on the model of this example. 



e* cos x 

 Put 



thus y = tan.~ l z, 



dy 1 dz 



therefore ~f = = -,- . 



dx l + z das 



... dz _ (e'cosa; e'smx)(l+e*sin#) e e cosx(e"cosx+e x smx} 



INOW j , r : TO 



cue (1 + e s 



_ e x (cos a; sin x e?) _ 



<fw & (cos a; sin x e*) 

 therefore -f- = -f- ^r^ -^ 



dx l + 2e sm x + e 



(10) y = sin x tan" 1 a? a* log x. 



du sin a: a z log # 



3r = cos x tan a; a log x H 



cte 



_,.,., , sin a; tan j x a" 



-f sin a; tan x a loga log x -\ -- . Art. 30. 



*c 



76. The differential coefficients of the simple functions are 

 here collected for the sake of reference. 



dy 

 -- 



--, - 

 dx x log e a 



