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Byju's Answer
Standard XII
Mathematics
Basic Inverse Trigonometric Functions
Solve y=tan...
Question
Solve
y
=
tan
−
1
5
a
x
a
2
−
6
x
2
, find
d
y
d
x
Open in App
Solution
y
=
tan
−
1
(
5
a
x
a
2
−
6
x
2
)
tan
y
=
5
a
x
a
2
−
6
x
2
∗
sec
2
y
−
tan
2
y
=
1
(
sec
2
y
)
d
y
d
x
=
5
a
(
a
2
−
6
x
2
)
−
(
−
12
x
)
(
5
a
x
)
(
a
2
−
6
x
2
)
2
[
1
+
(
5
a
x
a
2
−
6
x
2
)
2
]
d
y
d
x
=
5
a
3
−
30
a
x
2
+
60
a
x
2
(
a
2
−
6
x
2
)
2
[
a
4
+
36
x
4
+
13
a
2
x
2
(
a
2
−
6
x
2
)
2
]
d
y
d
x
=
5
a
3
+
30
a
x
2
(
a
2
−
6
x
2
)
2
[
(
a
4
)
+
36
x
4
+
13
a
2
x
2
]
d
y
d
x
=
5
a
(
a
2
+
6
x
2
)
(
a
2
+
9
x
2
)
(
a
2
+
4
x
2
)
d
y
d
x
=
5
a
(
a
2
+
6
x
2
)
∴
d
y
d
x
=
5
a
(
a
2
+
6
x
2
)
(
a
2
+
9
x
2
)
(
a
2
+
4
x
2
)
d
y
d
x
=
3
a
(
a
2
+
4
x
2
)
+
2
a
(
a
2
+
9
x
2
)
(
a
2
+
9
x
2
)
(
a
2
+
4
x
2
)
∴
d
y
d
x
=
3
a
a
2
+
9
x
2
+
2
a
a
2
+
4
x
2
Suggest Corrections
0
Similar questions
Q.
If
y
=
tan
−
1
(
5
a
x
a
2
−
6
x
2
)
, prove that:
d
y
d
x
=
3
a
a
2
+
9
x
2
+
2
a
a
2
+
4
x
2
.
Q.
Find
d
y
d
x
if
y
=
tan
−
1
(
5
x
+
1
3
−
x
−
6
x
2
)
.
Q.
Given
y
=
tan
−
1
5
x
1
−
6
x
2
,
−
1
√
6
<
x
<
1
√
6
, then find
d
y
d
x
.
Q.
Solve:
(
1
+
y
2
)
d
x
d
y
+
x
=
e
−
tan
−
1
y
Q.
Solve :
(
1
+
y
2
)
d
x
=
(
tan
−
1
y
−
x
)
d
y
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