求函数n阶导 求以下函数的n阶导数
\u6c42\u51fd\u6570\u7684n\u9636\u5bfc\u6570
\u5982\u56fe
=(1-(1-x^n))/(1-x)
=1/(1-x)-(1+x+\u2026+x^(n-1))
\u5176n\u9636\u5bfc\u4e0e1/(1-x)\u7684n\u9636\u5bfc\u76f8\u540c
这个求导需要多写几组找规律
由莱布尼兹公式：
y=(e^x)sinx的n阶导数
=(e^x)[sinx的n阶导数]+n(e^x)[sinx的n-1阶导数]+(1/2)n(n-1)(e^x)[sinx的n-2阶导数]+...+n(e^x)[sinx的1阶导数]+(e^x)sinx
=(e^x){[sinx的n阶导数]+n[sinx的n-1阶导数]+(1/2)n(n-1)[sinx的n-2阶导数]+...+n[sinx的1阶导数]+sinx}
=(e^x){[sin(x+nπ/2]+n[sin(x+(n-1)π/2]+(1/2)n(n-1)[sin(x+(n-2)π/2]+...+ncosx+sinx}。
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