if f(x) = (x^2-c^2)/(x^2+c^2) where c is a constant, find f'(x)

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if f(x) = (x^2-c^2)/(x^2+c^2) where c is a constant, find f'(x)

Mathematics
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\[f(x) = \frac {x^2-c^2}{x^2+c^2}\] simplify? \[f(x) = \frac {x^2+c^2-2c^2}{x^2+c^2} = 1 - \frac{2c^2}{x^2 + c^2}\] can you finish this?
i thought it would be \[\frac{ 2x-2c }{ 2x+2c }\]
why did you think that?

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hold on, i know what i did wrong
and remember, c is a constant so \(\frac{d}{dx} \left[ c^2 \right] = 0\)
\[\frac{ (x ^{2} +c ^{2})2x-(x ^{2{}}-c ^{2})2x}{ (x ^{2} +c ^{2})^{2}}\] is this right?
you are applying the quotient rule. before i look at your work, is that what you are supposed to be doing with this because it is a silly way to do it. it just adds complications. let me know either way and we can proceed
your application of the quotient rule is correct
if you wish to do it this way, next step is to simplify the numerator
simpliflying it would get me \[\frac{ 4xc ^{2} }{ (x ^{2}+c ^{2})^{2} }\]
well done!
so that's the answer?
yes
thank you!
mp

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