Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2009-01-19 08:52:26

LuisRodg
Real Member
Registered: 2007-10-23
Posts: 322

Proving the product rule of differentiation using induction.

Alright so I set out to prove this by induction:

And im stuck here. Could anyone offer some help? Please dont give me the full answer.

I would really appreciate some help.

Thanks!

Last edited by LuisRodg (2009-01-19 09:01:33)

Offline

#2 2009-01-19 18:04:40

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Proving the product rule of differentiation using induction.

I haven't checked over the work thoroughly, but it seems right.  You want to change the indices of the summations by changing ever occurrence of r to r - k.  Then your sum will be from k to n + k.  In your case, k = 1.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Offline

#3 2009-01-20 01:40:37

Kurre
Member
Registered: 2006-07-18
Posts: 280

Re: Proving the product rule of differentiation using induction.

Remember the formula c(n,k)=c(n-1,k)+c(n-1,k-1).

Offline

Board footer

Powered by FluxBB