f(x)=x/[x+(c/x)] can you please show all the steps please. Thanks
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Originally Posted by johntuan f(x)=x/[x+(c/x)] can you please show all the steps please. Thanks Is c a constant? If so $\displaystyle \frac{x}{x + \frac{c}{x}} = \frac{x}{\frac{x^2+c}{x}}= \frac{x^2}{x^2+c}$ Take the derivative of that $\displaystyle \frac{(2x)(x^2+c)~-~(2x)(x^2)}{(x^2+c)^2}$ Now just simplify $\displaystyle \frac{2cx}{(x^2+c)^2}$
Last edited by 11rdc11; Oct 13th 2008 at 11:25 AM.
You can use the quotient rule, but I don't quite remember it, so I'll just give you the necessary information. Top = x Derivative of the top= 1 Bottom = (x + c/x) Derivative of the bottom = 1 + -c/(x^2) Assuming that c is a constant.
i'm not sure if c is a constant but the answer is f'(x)=2cx/(x^2+c)^2
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