Question

求x^2*e^x的n阶导函数

Answer 1

y'=(x^2+2x)e^x

y"=(x^2+2x+2x+2)e^x=(x^2+4x+2)e^x

y"'=(x^2+4x+2+2x+4)e^x=(x^2+6x+6)e^x

y""=(x^2+6x+6+2x+6)e^x=(x^2+8x+12)e^x

y""'=(x^2+8x+12+2x+8)e^x=(x^2+10x+20)e^x

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y^(n)=[x^2+2nx+n(n-1)]e^x

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