Derivatives. 177 



2. (^j»f— .r-f- 1 j(^jfH- 1 j compare with example 6, Art. 19. 

 J. (x^-]rX-\-\)(x—i) compare with example 3, Art, 19. 



23. 'To FIND THE Derivative with Respect to x of the 

 Quotient of two Functions of .v.. 



Let u and 7' be the given functions of x, and let y be their quo- 

 tient, then we have 



d 



From (i), by multiplying by i\ we get 



u=vy, (2) 



hence D,./^=z'D,-j'+yD^z^, (t^) 



or J)ji=vTt,y-^~'T>,v. (^) 



Multiply both sides by v and we get 



TranvSposing and dividing by z"" we get 



Expressed in words this is 



The derivative of a fraction equals the denominator into the deriv- 

 ative of the numerator minus the numerator into the derivative of 

 the denominator all divided by the square of the defiomifiator. 



24. Examples. 



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

 pressions : 



x^-\- 1 



1. ' , compare with example 5, Art. 19. 



. -r^— 6.^''+ 11.^-— 6 ., , A 



2. — — — compare with example 4, Art. ig. 



■^ 3 



^' x'+i 

 x^i 

 ^' x^-f-i' 



A— 22 



