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UPSC NDA Math Model Paper 4
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© examsnet.com
Question : 26
Total: 120
Find
d
y
d
x
,
if
y
=
tan
−
1
[
8
x
1
−
15
x
2
]
5
1
+
25
x
2
−
3
1
+
9
x
2
5
1
+
25
x
2
+
3
1
+
9
x
2
8
1
+
25
x
2
None of these
Validate
Solution:
Given:
y
=
tan
−
1
[
8
x
1
−
15
x
2
]
y
=
tan
−
1
[
5
x
+
3
x
1
−
5
x
.
3
x
]
As we know that,
tan
−
1
x
+
tan
−
1
y
=
tan
−
1
[
x
+
y
1
−
x
y
]
So,
y
=
tan
−
1
[
5
x
+
3
x
1
−
5
x
.
3
x
]
=
tan
−
1
5
x
+
tan
−
1
x
Differentiating with respect to
x
, we get
d
y
d
x
=
d
(
tan
−
1
5
x
)
d
x
+
d
(
tan
−
1
3
x
)
d
x
=
5
1
+
(
5
x
)
2
+
3
1
+
(
3
x
)
2
=
5
1
+
25
x
2
+
3
1
+
9
x
2
© examsnet.com
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