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.
Hi all,
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.
Regards,
Shayne.
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.