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y=sin^4(x/4)+cos^4(x/4)求导数y=sin^4(x/4)+cos^4(x/4)=[sin^4(x/4)+cos^4(x/4)]'=4cos^3(x/4)-4sin^3(x/4)↑为什么不对?
题目详情
y=sin^4(x/4)+cos^4(x/4) 求导数
y=sin^4(x/4)+cos^4(x/4)
=[sin^4(x/4)+cos^4(x/4)]'
=4cos^3(x/4)-4sin^3(x/4)
↑为什么不对?
y=sin^4(x/4)+cos^4(x/4)
=[sin^4(x/4)+cos^4(x/4)]'
=4cos^3(x/4)-4sin^3(x/4)
↑为什么不对?
▼优质解答
答案和解析
错了
y=sin^4(x/4)+cos^4(x/4)
y'=[sin^4(x/4)+cos^4(x/4)]'
=4cos^3(x/4)-4sin^3(x/4)
这个是复合函数求导,里面的sin,cos也要求导,x/4还要求导
正确结果是:
y=sin^4(x/4)+cos^4(x/4)
y'=[sin^4(x/4)+cos^4(x/4)]'
=4sin^3(x/4)·cos(x/4)·1/4+4cos^3(x/4)·(-sin(x/4))·1/4
化简即可.
当然本题还有其他简便方法.
y=sin^4(x/4)+cos^4(x/4)
y'=[sin^4(x/4)+cos^4(x/4)]'
=4cos^3(x/4)-4sin^3(x/4)
这个是复合函数求导,里面的sin,cos也要求导,x/4还要求导
正确结果是:
y=sin^4(x/4)+cos^4(x/4)
y'=[sin^4(x/4)+cos^4(x/4)]'
=4sin^3(x/4)·cos(x/4)·1/4+4cos^3(x/4)·(-sin(x/4))·1/4
化简即可.
当然本题还有其他简便方法.
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