46 DIFFERENTIAL COEFFICIENTS. 



. 8y__ o 3 (a; 8 -4) 



6 dx~ V(a^-9* 4 +2'" 



-3(a: 2 -4) 



x VK^ 2 - 1) ( a - 4) 2 } x V( f - 1) ' 



4 3o; 2 

 In differentiating 3 we made use of the rule for 



C 



finding the differential coefficient of a fraction. By putting 

 the expression in the form 



x 1 x' 



that is, 4af 3 3af *, 



we obtain for the differential coefficient 

 -12af 4 +3af 2 , Art. 47, 



3(^-4) 

 or - i - , as above. 



It may be observed that cases of this kind frequently occur 

 in which we may adopt more than one method. The student 

 will find it very useful in rendering him familiar with the 

 rules, to obtain his results, if possible, by different methods. 



It is often convenient to take the logarithms of both sides of 

 an equation before differentiating. Thus, from the above, 

 we have 



lg y = \ (log <>> + lg x + log ( x 3a) log (x 4a) j. 



Take the differential coefficient of each member of the equa- 

 tion, therefore 



Idy 1 (1 1 1 ) 



___ -L = _ J __ j ____ _ Y 



y dx 2 (a; x 3a x 4aj 



a?-8ax + 12a z 

 ~ 2x(x-3a) (x-4a) ' 



