30 DIFFERENTIAL COEFFICIENT OF A LOGARITHM. 



hence by the rule just proved 



= of* c log, a. 

 Hence if y = e fx , 



_L fff* 

 dx~ 



and if y = e*, 



d y= e * 



dx 



50. Differential coefficient of log a x. 

 Let y = log a x, therefore 



therefore Ar/ = log a (x + h) Iog x 



therefore -~ 



x 



Assume A = xz, therefore 



y\/y; / % 



By Art. 19 the limit of ^" ^ when s diminishes 



z 



indefinitely is log a e, therefore 



dy 1 . 

 -f- = - log a e 

 dx x 



1 1 



Hence if y = log e x 



x ' log e a * 



^ 



dx x' 



