设f可导,y=sin{f[sin(x)]}且f(0)=0,求y'(0)

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设f可导,y=sin{f[sin(x)]}且f(0)=0,求y'(0)
设f可导,y=sin{f[sin(x)]}且f(0)=0,求y'(0)

设f可导,y=sin{f[sin(x)]}且f(0)=0,求y'(0)
y’=sin{f[sin(x)]}’
=cos{f【sin(x)]}*f ' [sin(x)]*cosx
则y‘(0)=cos{f【sin(0)]}*f ' [sin(0)]*cos0
又f ' [sin(0)]=f ’ (0)=0
所以y‘(0)=0