94 PRACTICAL MATHEMATICS 



dy du dv dw 

 (3) If ,- 



QJ- _ _ _ _ _ ..(_ _ _ 



?/ dx u dx v dx 



du dv 

 V fa~ U fa 



(6) Differentiating log e y with respect to x gives - -^ 



y dx 



60. The following examples will illustrate how the rules for 

 differentiation can be applied and how the table of standard 

 forms can be used : 



Example 1. Differentiate (1 )Vl + x 2 



(a) Treating it as a product and working with the rule 



dy dv du 



dx dx dx 



Then u = 1 x and -=- = 1 



dx 



v = (1 + x 2 ) 2 = s where z = 1 + a? 2 



, dz 



and = 2# 

 dx 



Then ^ = ^ ^ = 



