求sinx的n阶导数,麻烦给个过程
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求sinx的n阶导数,麻烦给个过程
![求sinx的n阶导数,麻烦给个过程](/uploads/image/z/17718647-23-7.jpg?t=%E6%B1%82sinx%E7%9A%84n%E9%98%B6%E5%AF%BC%E6%95%B0%2C%E9%BA%BB%E7%83%A6%E7%BB%99%E4%B8%AA%E8%BF%87%E7%A8%8B)
(sinx)'=cosx=sin(x+π/2)
(sinx)''=[sin(x+π/2)]'=cos[x+(π/2)]=sin[x+2(π/2)]
……
(sinx)^(n)=[sin(x+(n-1)(π/2))]'=cos[x+(n-1)(π/2)]=sin[x+n(π/2)]
(sinx)''=[sin(x+π/2)]'=cos[x+(π/2)]=sin[x+2(π/2)]
……
(sinx)^(n)=[sin(x+(n-1)(π/2))]'=cos[x+(n-1)(π/2)]=sin[x+n(π/2)]