Rationalised 2023-24
 MATHEMATICS
138
Example 35 Find 
2
2
d y
dx
, if  y = x3 + tan x Solution Given that y = x3 + tan x Then
dy
dx  = 3x2 + sec2 x
Therefore
2
2
d y
dx
 =
(
)
2
2
3
sec
d
x
x
dx
+
= 6x + 2 sec x sec x tan x = 6x + 2 sec2 x tan x
Example 36 If y = A sin x + B cos x, then prove that 
2
2
0
d y
y
dx
+
=