Well, let's see what you are doing?
Often, it is legal to use a little algebra to make your life easier. Compare your expression to . It's not quite the same thing, but it may be close enough.
The problem is to use the quotient rule to find the derivation of: f(x) = x / (x + (c/x))
I keep using the quotient rule over and over again with no success. Am I supposed to separately use the rule on c/x, and then use it on the whole function? Whether I am or not, could you please go through the problem step by step? I keep trying different ways to figure it out; I am unsure whether it is a problem with strategy or with algebra. Thanks.
Thanks. (Sorry, I don't know how to format mathematical equations on here)
f'(x) = x^2/(x^2 + c)
= (x^2 + c)(2x) - (x^2)(2x + 1) / (x^2 + c)^2
= 2x^3 + 2xc - 2x^3 - x^2 / (x^2 + c)^2
= (2xc - x^2) / (x^2 + c)^2
Is that right? Is it the final answer, or is there anything else I can do?