6 2 Rate of Change of Quantities
Recall that by the derivative ds
dt , we mean the rate of change of distance s with
respect to the time t In a similar fashion, whenever one quantity y varies with another
quantity x, satisfying some rule 
( )
y
=f x
, then dy
dx  (or f′(x)) represents the rate of
change of y with respect to x and  
dy
dx
x x

= 0
 (or f′(x0)) represents the  rate of change
of y with respect to x at 
0
x
=x if Further, if two variables x and y are varying with respect to another variable t, i