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根据导数定义求函数在指定点的导数: y=cosx,在x=π/4处
人气:116 ℃ 时间:2020-05-17 23:35:02
解答
△y=f(π/4+u)-f(π/4)=cos(π/4+u)-cosπ/4=-2sin(π/4+u/2)sin(u/2)
△x=u
y’=f’(π/4)
=(u→0)lim[-2sin(π/4+u/2)sin(u/2)/u]
=(u→0)lim[-sin(π/4+u/2)sin(u/2)/(u/2)]
=-sinπ/4
=-√2/2
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