Ok so I have found a formula for d^n/dx^n 1/x^2(adsbygoogle = window.adsbygoogle || []).push({});

= (-1)^n * (1+n)! * x^-(n+2)

So I have to do d/dx [(-1)^n * (1+n)! * x^-(n+2)] and see what I end up with. But how do I do that.

My book gives an example: (from d/dx (1+x)^-1)

d/dx [(-1)^k * k!(1+x)^(-k-1)] = (-1)^k * k!(-k-1)(1+x)^(-k-2)=...

What on earth is going on?! My book just drops explaning _how_ . Where does (-k-1) come from? I'm stuck...

Thanks

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# Proof by induction

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