If y = (tan–1 x)2, show that (x2 + 1)2 y2 + 2x (x2 + 1) y1 = 2
Miscellaneous Examples
Example 39 Differentiate w r t x, the following function:
(i)
12
3
2
2
4
x
x
+
+
+
(ii)    log7 (log x)
Solution
(i)
Let y = 
12
3
2
2
4
x
x
+
+
+
= 
1
1
2
2
2
(3
2)
(2
4)
x
x
−
+
+
+
Note that this function is defined at all real numbers 
x > −32