It is just the general power rule for derivatives but you need to use some algebra first.
You could also use the quotient rule but that would be way too much work.
I have been asked to differentiate the function where . I have not been asked previously in exercises (or taught for that matter) how to differentiate fractions like this. I have used Mathcad to find the solution hoping it would reveal a method to me, but with no such luck. I would really appreciate any help on this. I think it may be a rule for powers prior to finding the derivative that I am missing.
I'm not sure I agree that the quotient rule is SO much more work. I often find that it's a bit more calculus up front, but can somtimes be less algebra later. My working:
Where I especially see a savings in effort is when taking derivatives of functions like this:
If you flip the denominator upstairs and use the product rule, you'll have to turn right around, often, and get a common denominator. Using the quotient rule saves you that step.
My two cents.