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Byju's Answer
Standard XII
Mathematics
Integration Using Substitution
Differentiate...
Question
Differentiate the following functions w.r.t.
x
:
sin
−
1
(
1
−
x
2
)
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Solution
Let
y
=
sin
−
1
(
1
−
x
2
)
Differentiate on both sides w.r.t. x
d
y
d
x
=
1
√
1
−
(
1
−
x
2
)
2
d
d
x
(
1
−
x
2
)
=
−
2
x
√
2
x
2
−
x
4
−
1
≤
1
−
x
2
≤
1
;
2
≥
x
2
≥
0
;
x
ϵ
[
−
√
2
≤
x
≤
√
2
]
∴
d
y
d
x
=
−
2
x
|
x
|
√
2
−
x
2
,
(
−
√
2
≤
x
≤
√
2
)
∴
d
y
d
x
=
⎧
⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪
⎩
2
√
2
−
x
2
,
−
√
2
≤
x
≤
0
−
2
√
2
−
x
2
,
0
<
x
≤
√
2
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