To answer the first question write down the derivative of the product of two function and three functions. Do you nottice a pattern? Thus, what can you conclude for functions?
Have you found a proof by induction for the second question now?
Three steps are involved in Mathematical induction. Step 1: check that the statement is true for n = 1
Step 2: take that the statement is true for n = k
Step - 3: Prove that the statement is true for n = k+1 when it is true for n = k
If the first and last step are true i.e., the statement is true for n = 1 and statement being true for n=k implies that the statement is true for n = k+1 the we say the the statement is true for all values of n.
Thanks.... I was never taught induction in my Precalc class, school schedule was tight so they unfortunately had to make cuts to the curriculum. I get the idea now, thanks for the help!
Also I should have reworded this post.. I didn't want to seem that this was a HW that I had to do. I'm just interested in the concepts that make calculus work. I'll just be careful in wording posts from now on (I'll attempt the problem first). Again, sorry if it seems that I'm coming for solutions for my HW. I'm not. I'm just a little curious and I want to go beyond the textbook.