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Mathematics
Problem
If
y
=
a
cos
−
1
x
1
+
a
cos
−
1
x
y = \frac{a^{\cos^{-1} x}}{1 + a^{\cos^{-1} x}}
y
=
1
+
a
c
o
s
−
1
x
a
c
o
s
−
1
x
and
z
=
a
cos
−
1
x
z = a^{\cos^{-1} x}
z
=
a
c
o
s
−
1
x
, then
d
y
d
z
=
\frac{dy}{dz} =
d
z
d
y
=
(a)
1
1
+
a
cos
−
1
x
\frac{1}{1 + a^{\cos^{-1} x}}
1
+
a
c
o
s
−
1
x
1
(b)
−
1
1
+
a
cos
−
1
x
-\frac{1}{1 + a^{\cos^{-1} x}}
−
1
+
a
c
o
s
−
1
x
1
(c)
1
(
1
+
a
cos
−
1
x
)
2
\frac{1}{(1 + a^{\cos^{-1} x})^2}
(
1
+
a
c
o
s
−
1
x
)
2
1
(d) None of these
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