amy0799
  • amy0799
if f(x) = (x^2-c^2)/(x^2+c^2) where c is a constant, find f'(x)
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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IrishBoy123
  • IrishBoy123
\[f(x) = \frac {x^2-c^2}{x^2+c^2}\] 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?
amy0799
  • amy0799
i thought it would be \[\frac{ 2x-2c }{ 2x+2c }\]
IrishBoy123
  • IrishBoy123
why did you think that?

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amy0799
  • amy0799
hold on, i know what i did wrong
IrishBoy123
  • IrishBoy123
and remember, c is a constant so \(\frac{d}{dx} \left[ c^2 \right] = 0\)
amy0799
  • amy0799
\[\frac{ (x ^{2} +c ^{2})2x-(x ^{2{}}-c ^{2})2x}{ (x ^{2} +c ^{2})^{2}}\] is this right?
IrishBoy123
  • IrishBoy123
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
IrishBoy123
  • IrishBoy123
your application of the quotient rule is correct
IrishBoy123
  • IrishBoy123
if you wish to do it this way, next step is to simplify the numerator
amy0799
  • amy0799
simpliflying it would get me \[\frac{ 4xc ^{2} }{ (x ^{2}+c ^{2})^{2} }\]
IrishBoy123
  • IrishBoy123
well done!
amy0799
  • amy0799
so that's the answer?
IrishBoy123
  • IrishBoy123
yes
amy0799
  • amy0799
thank you!
IrishBoy123
  • IrishBoy123
mp

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