OF AN IMPLICIT FUNCTION. 159 



Thus (2) becomes 



cPu 



or 



p + (I) - 1- that is 



this simplification we obtain the required result. 

 A very common mistake is to omit the brackets in 



remains a superfluous term, namely --, ,- , or as it has perhaps 

 been written by the student, 



183. In Art. 182 we proceeded very strictly according to 

 the literal requirements of the rule involved in equation (2) of 

 Art. 181. We might have reasoned thus. 



We have merely to express symbolically the fact, that the 

 differential coefficient of 



fdu\ dy (du\ 

 \dy) dx \dx) 



with respect to x is zero. 



Now the differential coefficient of (-7- J with respect to x 



( d*u \ fd?u\ dy 

 , I _ ] _L _ a . 



_ _ _ 

 \dx dy) \difj dx ' 



and the differential coefficient of -/- with respect to x is -^ . 



dx ax 



