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Byju's Answer
Standard XII
Mathematics
Differentiation Using Substitution
If y =tan -15...
Question
If
y
=
t
a
n
−
1
5
x
1
−
6
x
2
,
−
1
√
6
<
x
<
1
√
6
,
then prove that
d
y
d
x
=
2
1
+
4
x
2
+
3
1
+
9
x
2
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Solution
Here
y
=
t
a
n
−
1
5
x
1
−
6
x
2
=
t
a
n
−
1
(
3
x
+
2
x
1
−
3
x
.2
x
)
=
t
a
n
−
1
3
x
+
t
a
n
−
1
2
x
⇒
d
y
d
x
=
d
d
x
(
t
a
n
−
1
3
x
+
t
a
n
−
1
2
x
)
∴
d
y
d
x
=
3
1
+
9
x
2
+
2
1
+
4
x
2
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