Solution Let 
2
2
(
3) (
4)
(3
4
5)
x
x
y
x
x
−
+
=
+
+
Taking logarithm on both sides, we have
log y = 1
2 [log (x – 3) + log (x2 + 4) – log (3x2 + 4x + 5)]
Now, differentiating both sides w r t x, we get
1 dy
y dx
⋅
 =
2
2
1
1
2
6
4
2 (
3)
4
3
4
5
x
x
x
x
x
+x


+
−


−
+
+
+


or
dy
dx  =
2
2
1
2
6
4
2
(
3)
4
3
4
5
y
x
x
x
x
x
+x


+
−


−
+
+
+


=
2
2
2
2
1
(
3)(
4)
1
2
6
4
2
(
3)
3
4
5
4
3
4
5
x
x
x
x
x
x
x
x
x
x
−
+
+


+
−


−
+
+
+
+
+


Example 28 Differentiate ax w