I have a function that I want to find the derivative of using the difference quotient definition of a derivative. The function is:
therefore, using the difference quotient definition, we have:
this is equal to:
I tried using (a+b)(a-b) = a^2 - b^2 to get rid of the square roots in the numerator, but the denominator gets pretty huge, so I'm not sure if this is a wise path to proceed down.
At this point I get stuck with the algebra. I understand that this is a simple derivative to take using the quotient rule, but I'm trying to practice taking limits, and to learn useful algebra tricks.
A step by step computation would be helpful. Many thanks