,
( )
x
=f t
and 
( )
y
=g t
, then by Chain Rule
dy
dx  = dy
dx
dt
dt ,  if  
0
dx
dt ≠
Chapter 6
APPLICATION OF
DERIVATIVES
Rationalised 2023-24
 MATHEMATICS
148
Thus, the rate of change of y with respect to x can be calculated using the rate of
change of y and that of x both with respect to t Let us consider some examples Example 1 Find the rate of change of the area of a circle per second with respect to
its radius r when r = 5 cm Solution The area A of a circle with radius r is given by A = πr2