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Mathematics
Mathematics
Problem
If
y
=
tan
−
1
(
x
1
/
3
+
a
1
/
3
1
−
x
1
/
3
a
1
/
3
)
y = \tan^{-1} \left( \frac{x^{1/3} + a^{1/3}}{1 - x^{1/3} a^{1/3}} \right)
y
=
tan
−
1
(
1
−
x
1/3
a
1/3
x
1/3
+
a
1/3
)
, then
d
y
d
x
=
\frac{dy}{dx} =
d
x
d
y
=
(a)
1
3
x
2
/
3
(
1
+
x
2
/
3
)
\frac{1}{3x^{2/3}(1+x^{2/3})}
3
x
2/3
(
1
+
x
2/3
)
1
(b)
a
3
x
2
/
3
(
1
+
x
2
/
3
)
\frac{a}{3x^{2/3}(1+x^{2/3})}
3
x
2/3
(
1
+
x
2/3
)
a
(c)
−
1
3
x
2
/
3
(
1
+
x
2
/
3
)
-\frac{1}{3x^{2/3}(1+x^{2/3})}
−
3
x
2/3
(
1
+
x
2/3
)
1
(d)
−
a
3
x
2
/
3
(
1
+
x
2
/
3
)
-\frac{a}{3x^{2/3}(1+x^{2/3})}
−
3
x
2/3
(
1
+
x
2/3
)
a
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