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Byju's Answer
Standard XII
Mathematics
Chain Rule of Differentiation
Let y = log...
Question
Let
y
=
log
sin
(
x
2
)
,
0
<
x
≤
π
2
. The value of
d
y
d
x
at
x
=
√
π
2
is:
A
0
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B
1
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C
π
−
4
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D
√
π
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Solution
The correct option is
D
√
π
y
=
log
sin
(
x
2
)
Chain rule leads us to
d
y
d
x
=
1
sin
(
x
2
)
×
cos
(
x
2
)
×
2
x
Substituting
x
as
√
π
2
, we get
d
y
d
x
=
cot
π
4
×
√
π
=
√
π
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0
Similar questions
Q.
Let
y
=
y
(
x
)
be the solution of the differential equation,
d
y
d
x
+
y
tan
x
=
2
x
+
x
2
tan
x
,
x
∈
(
−
π
2
,
π
2
)
, such that
y
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=
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Then :
Q.
If
x
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2
t
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1
+
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2
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and
y
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b
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(
1
−
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t
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, find the values of
d
y
d
x
at
t
=
π
4
and
t
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3
OR
If
y
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x
x
, prove that
d
2
y
d
x
2
−
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y
(
d
y
d
x
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Q.
If
y
=
cot
−
1
√
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+
sin
x
+
√
1
−
sin
x
√
1
+
sin
x
−
√
1
−
sin
x
, find
d
y
d
x
if
x
∈
(
0
,
π
2
)
∪
(
π
2
,
π
)
Q.
Let
y
=
∣
∣
∣
tan
(
π
4
−
x
)
∣
∣
∣
. Then
d
y
d
x
at
x
=
π
4
Q.
Let
y
=
√
(
c
o
s
x
+
c
o
s
2
x
+
c
o
s
3
x
)
2
+
(
s
i
n
x
+
s
i
n
2
x
+
s
i
n
3
x
)
2
.
Then which of the following statements are correct?
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