Find the 500th derivative of...
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Find the 500th derivative of...

[From: ] [author: ] [Date: 12-10-02] [Hit: ]
......
f(x)=xe^-x

Any steps would be appreciated, thank you.

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f'(x) = e^-x + x(-e^-x) {Found by product rule}
f'(x) = e^-x - xe^-x

f''(x) = -e^-x -(e^-x - xe^-x) {as we already know the derivative of xe^-x}
f''(x) = -2e^-x + xe^-x

I'm sure you can see the pattern here. All you have to notice are the sign switches at odd and even, and the leading coefficient IS the derivative number.
f(500)(x) = -500e^-x + xe^-x
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