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Mathematics
Problem
If
y
=
x
+
1
x
+
1
x
+
1
x
+
…
∞
y = x + \frac{1}{x + \frac{1}{x + \frac{1}{x + \dots \infty}}}
y
=
x
+
x
+
x
+
x
+
…
∞
1
1
1
, prove that
d
y
d
x
=
y
(
2
y
−
x
)
\frac{dy}{dx} = \frac{y}{(2y - x)}
d
x
d
y
=
(
2
y
−
x
)
y
.
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