关于隐函数导数问题y(x)满足y+siny=ln(1-(tanx)^2),求y''(0)=?

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关于隐函数导数问题y(x)满足y+siny=ln(1-(tanx)^2),求y''(0)=?
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关于隐函数导数问题y(x)满足y+siny=ln(1-(tanx)^2),求y''(0)=?
关于隐函数导数问题
y(x)满足y+siny=ln(1-(tanx)^2),求y''(0)=?

关于隐函数导数问题y(x)满足y+siny=ln(1-(tanx)^2),求y''(0)=?
y+siny = ln[1-tan²(x)] (1)
y' + y'cosy = -2tan(x) sec² x/(1-tan²x) (2)
y' = -2tan(x) sec² x / [(1-tan²x)(1+cosy)] (3)
y''+y''cosy-y'²siny = -2(sec²xcos 2x + 2tanx sin 2x)/cos²2x (4)
不用解出:y"的具体表达式,将 x=0; y(0)=y'(0)=0 代入(4)式,
解出:y"(0) = -1 (5)