( )
dxd f x
 =
3
(2
1)
d
x
dx


+


=
3
2
(8
12
6
1)
d
x
x
x
dx
+
+
+
= 24x2 + 24x + 6
= 6 (2x + 1)2
Now, observe that
f (x) = (h o g) (x)
where g(x) = 2x + 1 and h(x) = x3 Put t = g(x) = 2x + 1 Then f(x) = h(t) = t3 Thus
df
dx  =
6 (2x + 1)2 = 3(2x + 1)2