1. ## Quotient Rule Problem

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.

2. 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 $\displaystyle \frac{x^{2}}{x^{2}+c}$. It's not quite the same thing, but it may be close enough.

3. Originally Posted by Maziana
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.
since x cannot equal 0, multiply numerator and denominator by x ...

$\displaystyle f(x) = \frac{x^2}{x^2+c}$

now use the quotient rule

4. 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?

5. There's your problem: $\displaystyle \frac{d}{dx}(Constant)\;=\;0$

You have: $\displaystyle \frac{d}{dx}(c)\;=\;1$ -- No good.

See how quickly we can get to the heart of the problem when the student shows the work?

6. You're right; I was thinking of it as a variable. Thanks so much.