Induction for Nth derivative of a product
Posted by peeterjoot on January 2, 2012
I had use for the result , where , and felt like doing the induction.
Let’s look at the first few cases, starting with . That’s just the chain rule
For we have
The induction hypothesis is clearly of the form of a binomial product
Let’s try the induction
Simplification of the binomial coefficients should finish the job
Assembling the terms we have
which completes the induction.