`f(x) = (c^2 - x^2)/(c^2 + x^2)`

`f'(x) = {-2x(c^2 + x^2) - 2x(c^2 - x^2)}/(c^2 + x^2)^2`

`or, f'(x) = (-4xc^2)/(c^2+x^2)^2`

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