Derivatives. i8i 



29. I'o FIND THE Derivative with Respect to .v of a 

 Fractional Power of x. 



p 

 Multiply the left membei by z and the right member by ;f<', 



which is the equal of z, and we obtain 



p A-: 



D,,2'=-:t-^ 

 The same reasoning would show that \i y^=ax'' , then 



Hence, as in the two preceding articles, the result is obtained 

 by multiplying- the exponent by the coefficient and reducing the ex- 

 p07ient I. 



30. Examples. 



Find the derivative with respect to x of the following expres- 

 sions : 



1. (x'-—x-\-i)-\-2(x^—x-\-i). 



\x-'—i] , i^-'—i] 



2, I I +2 ■ , 

 LJtr+i I Ur+lJ 



4 p— I 



5. {x-\-sJ i-x')". 



