differentiate w.r.t.x.
[(tanx)^tanx]^tanx at x=π/4
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Answer:
Consider the following differential eq.
y=((tanx)
tanx
)
tanx
&x=
4
π
Taking log both side, we get.
logy=tan
2
xlog(tanx)
Differentiate both side w.r.t x, we get.
y
1
dx
dy
=2tanxsec
2
xlog(tanx)+tan
2
x
tanx
1
sec
2
x
y
1
dx
dy
=((tanx)
tanx
)
tanx
(2tan
4
π
sec
2
4
π
log(tan
4
π
)+tan
4
π
sec
2
4
π
)
dx
dy
=0+2
=2
Hence, this is the required answer.
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