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Mathematics
Mathematics
Problem
Which of the following is/are true? (a)
d
y
d
x
\frac{dy}{dx}
d
x
d
y
for
y
=
sin
−
1
(
cos
x
)
y=\sin^{-1}(\cos x)
y
=
sin
−
1
(
cos
x
)
, where
x
∈
(
0
,
π
)
x\in(0,\pi)
x
∈
(
0
,
π
)
, is
−
1
-1
−
1
(b)
d
y
d
x
\frac{dy}{dx}
d
x
d
y
for
y
=
sin
−
1
(
cos
x
)
y=\sin^{-1}(\cos x)
y
=
sin
−
1
(
cos
x
)
, where
x
∈
(
π
,
2
π
)
x\in(\pi,2\pi)
x
∈
(
π
,
2
π
)
, is
1
1
1
(c)
d
y
d
x
\frac{dy}{dx}
d
x
d
y
for
y
=
cos
−
1
(
sin
x
)
y=\cos^{-1}(\sin x)
y
=
cos
−
1
(
sin
x
)
, where
x
∈
(
−
π
2
,
π
2
)
x\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)
x
∈
(
−
2
π
,
2
π
)
, is
−
1
-1
−
1
(d)
d
y
d
x
\frac{dy}{dx}
d
x
d
y
for
y
=
cos
−
1
(
sin
x
)
y=\cos^{-1}(\sin x)
y
=
cos
−
1
(
sin
x
)
, where
x
∈
(
π
2
,
3
π
2
)
x\in\left(\frac{\pi}{2},\frac{3\pi}{2}\right)
x
∈
(
2
π
,
2
3
π
)
, is
−
1
-1
−
1
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