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KEAM 2015 Math Paper
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© examsnet.com
Question : 114
Total: 120
If
y
2
=
100
t
a
n
−
1
x
+
45
s
e
c
−
1
x
+
100
c
o
t
−
1
x
+
45
c
o
s
e
c
−
1
x
,
then
d
y
d
x
=
x
2
−
1
x
2
+
1
x
2
+
1
x
2
−
1
1
0
1
x
√
x
2
−
1
Validate
Solution:
y
2
=
100
tan
−
1
x
+
45
sec
−
1
x
+
100
cot
−
1
x
+
45
cosec
−
1
x
=
100
tan
−
1
x
+
100
cot
−
1
x
+
45
sec
−
1
x
+
45
cosec
−
1
x
=
100
(
tan
−
1
x
+
cot
−
1
x
)
+
45
(
sec
−
1
x
+
cosec
−
1
x
)
=
100
×
π
2
+
45
×
π
2
On differentiating both sides w.r.t.
x
,
we get
2
y
y
′
=
0
⇒
y
′
=
0
[
∵
2
≠
0
,
y
≠
0
]
© examsnet.com
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