y=sin^4x/4+cos^4x的导数怎么求?
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y=sin^4x/4+cos^4x的导数怎么求?
打错了,是y=sin^4(x/4)+cos^4(x/4)
打错了,是y=sin^4(x/4)+cos^4(x/4)
![y=sin^4x/4+cos^4x的导数怎么求?](/uploads/image/z/8644905-9-5.jpg?t=y%3Dsin%5E4x%2F4%2Bcos%5E4x%E7%9A%84%E5%AF%BC%E6%95%B0%E6%80%8E%E4%B9%88%E6%B1%82%3F)
y=sin^4(x/4)+cos^4(x/4)
=[sin^2(x/4)+cos^2(x/4)]^2-2sin^2(x/4)cos^2(x/4)
=1-1/2sin^2(x/2)
=1-1/4(1-cosx)
=3/4+1/4cosx
y′=-1/4sinx
=[sin^2(x/4)+cos^2(x/4)]^2-2sin^2(x/4)cos^2(x/4)
=1-1/2sin^2(x/2)
=1-1/4(1-cosx)
=3/4+1/4cosx
y′=-1/4sinx
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