DIFFERENTIATION OF A CONSTANT. 21 



33. Differentiation of a constant. 

 If y = c where c is a constant, then ~ = 0. For to say 



that y is equal to a constant is the same thing as saying that 

 y cannot vary ; hence Ay = 0, therefore 



whatever be the value of Aa; ; therefore 



^y n 



dx 

 Hence, making < (a;) = a constant c in Art. 29, we have 



This may of course be obtained directly thus : 

 Let u = C'fy((K), 



then w + AM = 



,, r. Aw >Jr( 



therefore -T = c J - 



Aa; 



therefore -^- = c-v/r' fa;) . 



aaj 



So by putting < (a;) = c in Art. 31, we obtain 

 , c c-v/r' (a;) 



~ 



which likewise may be found independently. 



34. We have now defined a differential coefficient and 

 have shewn how the differential coefficient of a compound 

 function can be found as soon as we know the differential 

 coefficients of the component functions. Before we proceed 

 to the rules for determining the differential coefficient of any 

 known algebraical expression, we shall give some geometrical 

 illustrations which will assist in forming a conception of the 

 meaning of a differential coefficient and afford some hints as 

 to the applications which can be made of the doctrine of 

 limits. 



