168 EVALUATION OF DIFFERENTIAL COEFFICIENTS 



Again, suppose ay* bx*y+x'= to be the given equation. 

 Then 



therefore 



This value of -^- takes the form - when x and y vanish. 

 ax 



Hence, differentiating the numerator and denominator, we 

 have 



flfiC flfy 



2 foe 6a?/ -j^- 

 when a; and y are made = 0. 



Again, we have the form - . Hence, differentiating again, 



24* -45^- 

 dy _ dx 



~~ 



y 

 x and y being made each = 0. Thus assuming that x -^ 



and y -j vanish, we have 



. 



dx 



from which -^ = 0, 



aa; 





193. It may be noticed that equation (2) of Art. 190 

 differs from equation (3) of Art. 181 only in the omission of 



