求y=[sin^2(3x+π/4)]的导数,

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求y=[sin^2(3x+π/4)]的导数,求y=[sin^2(3x+π/4)]的导数,求y=[sin^2(3x+π/4)]的导数,y是2次复合y=u^2u=sinvv=3x+π/4y''=2u*u''*

求y=[sin^2(3x+π/4)]的导数,
求y=[sin^2(3x+π/4)]的导数,

求y=[sin^2(3x+π/4)]的导数,
y是2次复合
y=u^2
u=sinv
v=3x+π/4
y'=2u*u'*v'
∴y'=2sin(3x+π/4)*cos(3x+π/4)*(3x+π/4)'
=2sin(3x+π/4)*cos(3x+π/4)*3
=3*2sin(3x+π/4)cos(3x+π/4).
=3sin(6x+π/2).正弦二倍角公式
=3cos6x