## amy0799 one year ago if f(x) = (x^2-c^2)/(x^2+c^2) where c is a constant, find f'(x)

1. 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?

2. amy0799

i thought it would be $\frac{ 2x-2c }{ 2x+2c }$

3. IrishBoy123

why did you think that?

4. amy0799

hold on, i know what i did wrong

5. IrishBoy123

and remember, c is a constant so $$\frac{d}{dx} \left[ c^2 \right] = 0$$

6. amy0799

$\frac{ (x ^{2} +c ^{2})2x-(x ^{2{}}-c ^{2})2x}{ (x ^{2} +c ^{2})^{2}}$ is this right?

7. 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

8. IrishBoy123

your application of the quotient rule is correct

9. IrishBoy123

if you wish to do it this way, next step is to simplify the numerator

10. amy0799

simpliflying it would get me $\frac{ 4xc ^{2} }{ (x ^{2}+c ^{2})^{2} }$

11. IrishBoy123

well done!

12. amy0799

13. IrishBoy123

yes

14. amy0799

thank you!

15. IrishBoy123

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