SUCCESSIVE DIFFERENTIATION. 59 



79. Suppose y = d\ 



therefore ~ = a x log a. 



dx 



d n y 

 and ~Z=a x (loga) n . 



Similarly, if y = e M , V^ = V*. 



If y = log x, 



^-i-ofi 



i * > 

 ao; a; 



*S f 



dx* X ' 



$y -* 



_ iZ. Q/y. S 

 t& 8 ~ ' ' 



B -- 



where }n 1 stands for 1 . 2.3 ... (n 1). 



80. Differential coefficient of the product of two functions. 

 Suppose u yz, 



where y and z are functions of x ; we have 



du _ dz dy 

 dx y dx dx 



Differentiating both sides of the equation with respect to 

 x, we have 



d*u d*z dy dz dy dz d*y 



_ -_ *y _ ^| n _ i _.-,_. ^ ^*^ --i- _1_ ^ / 



* 1 ' 



dx* 



d*z dy dz d*y 

 - ~ Z 



