I can't figure out where I went wrong in finding the derivative for this function. Can anyone spot my error?
$2(x^2 + y^2)^2 = 25(x^2 - y^2)$
$4(x^2 + y^2)(2x + 2yy') = 25(2x - 2yy')$
$\displaystyle \frac{2x + 2yy'}{2x - 2yy'} = \frac{25}{4(x^2 + y^2)}$
$2x + 2yy' = 25$
$\displaystyle y' = \frac{25 - 2x}{2y}$
On the initial line is the function I'm differentiating; the rest is the process of differentiation.
$$4(x^2+y^2)2(x+y')=25\cdot2(x-y')$$
$$\frac{x+y'}{x-y'}=\frac{25}{4(x^2+y^2)}$$
Applying Componendo and dividendo,
$$\frac{y}x'=\frac{25-4(x^2+y^2)}{25+4(x^2+y^2)}$$