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Mathematics
Mathematics
Problem
If
y
=
(
sin
x
)
(
sin
x
)
(
sin
x
)
…
∞
y = (\sin x)^{(\sin x)^{(\sin x)^{\dots\infty}}}
y
=
(
sin
x
)
(
s
i
n
x
)
(
s
i
n
x
)
…
∞
, prove that
d
y
d
x
=
y
2
cot
x
(
1
−
y
log
sin
x
)
\frac{dy}{dx} = \frac{y^2 \cot x}{(1 - y \log \sin x)}
d
x
d
y
=
(
1
−
y
l
o
g
s
i
n
x
)
y
2
c
o
t
x
.
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