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# Nth derivative watch

1. Say we want to find the (2m+1)th derivative of .

By some appropriate method, we can show that:

.

Can we do the following? Replace n with (2m+1), and we have:

.

It seems completely valid to me, but I can't afford to be wrong.
2. (Original post by Wannalearn)
Say we want to find the (2m+1)th derivative of .

By some appropriate method, we can show that:

.

Can we do the following? Replace n with (2m+1), and we have:

.

It seems completely valid to me, but I can't avoid to be wrong.
You can simplify your first formula to

But yes, you can replace n with 2m+1. What that's saying is your formula is valid for all natural numbers hence it's valid for all positive odd numbers. However if you're being formal then you would need to say that n and m are natural and you would need to have proven the first formula, say, by induction.

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Updated: November 28, 2010
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