求导数y=arctan(2tanx/2)

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求导数y=arctan(2tanx/2)
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求导数y=arctan(2tanx/2)
求导数y=arctan(2tanx/2)

求导数y=arctan(2tanx/2)
y'=1/[1+(2tanx/2)²]*(2tanx/2)'
=1/[1+(2tanx/2)²]*2sec²(x/2)*(x/2)'
=1/[1+(2tanx/2)²]*sec²(x/2)
=1/cos²(x/2)*1/[1+4sin²(x/2)/cos²(x/2)]
=1/[cos²(x/2)+4sin²(x/2)]
=1/[1+3(1-cosx)/2]
=2/(5-cosx)

y=arctan(2tan(x/2))
tany = 2tan(x/2)
(secy)^2y' = [sec(x/2)]^2
(1+4[tan(x/2)]^2)y' = [sec(x/2)]^2
y' =[sec(x/2)]^2/{1+4[tan(x/2)]^2}