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.
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.