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

Question

irishboy123 · Answer

$$f(x) = \frac {x^2-c^2}{x^2+c^2}$$
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 · Answer

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

irishboy123 · Answer

why did you think that?

amy0799 · Answer

hold on, i know what i did wrong

irishboy123 · Answer

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

amy0799 · Answer

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

irishboy123 · Answer

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 · Answer

your application of the quotient rule is correct

irishboy123 · Answer

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

amy0799 · Answer

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

irishboy123 · Answer

well done!

amy0799 · Answer

so that's the answer?

irishboy123 · Answer

yes

amy0799 · Answer

thank you!

irishboy123 · Answer

mp