I always find it much easier to put a rational function into a product when I need to differentiate but I am trying to work on using the quotient rule.

the function is

if I use the product rule after making it a product it is pretty easy to obtain

but when I try to use the quotient rule it isn't as simple

I think I have the work correct in this

Thanks! I know it seems like a pointless post but I just want to make sure my sequence is correct.