having problems with the following problem:

Consider,

Use the principle of induction to prove that forn>=1 the derivative of is:

if anyone could show me how to solve this problem it would be much appreciated.

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- Sep 30th 2009, 07:13 PMJonny-123Induction Problem
having problems with the following problem:

Consider,

Use the principle of induction to prove that for*n>=*1 the derivative of is:

if anyone could show me how to solve this problem it would be much appreciated. - Sep 30th 2009, 07:44 PMTheEmptySet
note that

First verify the base case when n=1

So the base case checks

Now we assume it is true for n and show n+1

Now take the derivative of the induction hypothsis to get

lets simplify a bit

and now factor out a 2 to get

but this isn't quite what we want so lets build the fraction by multiplying by (n+1)

and we are done.