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Byju's Answer
Standard XII
Mathematics
First Principle of Differentiation
Find the deri...
Question
Find the derivative of
sin
(
2
sin
−
1
x
)
.
A
2
cos
(
2
sin
−
1
x
)
√
1
−
x
2
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B
cos
(
2
sin
−
1
x
)
√
1
−
x
2
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C
2
cos
(
2
cos
−
1
x
)
√
1
−
x
2
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D
−
cos
(
2
cos
−
1
x
)
√
1
−
x
2
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Solution
The correct option is
A
2
cos
(
2
sin
−
1
x
)
√
1
−
x
2
We need to find derivative of
sin
(
2
sin
−
1
x
)
Apply the chain rule,
Let
f
=
sin
(
u
)
Therefore,
d
d
x
(
sin
(
2
arcsin
(
x
)
)
)
=
d
d
u
(
sin
(
u
)
)
d
d
x
(
2
arcsin
(
x
)
)
We know that
d
d
u
(
sin
(
u
)
)
=
cos
(
u
)
and
d
d
x
(
2
arcsin
(
x
)
)
=
2
d
d
x
(
arcsin
(
x
)
)
=
2
⋅
1
√
1
−
x
2
So,
d
d
x
(
sin
(
2
arcsin
(
x
)
)
)
=
d
d
u
(
sin
(
u
)
)
d
d
x
(
2
arcsin
(
x
)
)
=
cos
(
u
)
2
√
1
−
x
2
=
cos
(
2
arcsin
(
x
)
)
2
√
1
−
x
2
=
2
cos
(
2
arcsin
(
x
)
)
√
1
−
x
2
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