y=sin(x+y)求y''(隐式函数二阶导)

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y=sin(x+y)求y''(隐式函数二阶导)

y=sin(x+y)求y''(隐式函数二阶导)
y=sin(x+y)求y''(隐式函数二阶导)

y=sin(x+y)求y''(隐式函数二阶导)
y'=[sin(x+y)]'(x+y)'=(1+y')cos(x+y)=cos(x+y)+y'cos(x+y)
y'=cos(x+y)/[(1-cos(x+y)]
y''=[cos(x+y]'(x+y)'+y''cos(x+y)+y'[cos(x+y)]'
=-(1+y')sin(x+y)+y''cos(x+y)-y'(1+y')sin(x+y)
y''[cos(x+y)-1]=(1+y')^2sin(x+y)
={1+cos(x+y)/[(1-cos(x+y)]}^2sin(x+y)
=sin(x+y)/[cos(x+y)-1]^2
y''=sin(x+y)/[cos(x+y)-1]^3

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