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)](/uploads/image/z/18342671-23-1.jpg?t=%E8%AE%BEf%E5%8F%AF%E5%AF%BC%2Cy%3Dsin%7Bf%5Bsin%EF%BC%88x%EF%BC%89%5D%7D%E4%B8%94f%EF%BC%880%EF%BC%89%3D0%2C%E6%B1%82y%27%280%29)
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
=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
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