So recently I was reviewing calculus, and I tried to differentiate the equation: $(x^2-y^2)/(x^2+y^2)=1/2$
The first thing I did was make the equation easier to differentiate by multiplying the whole equation by $(x^2+y^2)$ to get $x^2-y^2=(1/2)x^2+(1/2)y^2$ Then I differentiated: $d/dx (x^2-y^2)=d/dx((1/2)x^2+(1/2)y^2)$ This should differentiate to: $2x-2yy'=x+yy'$ Then I simplified it to: $x=3yy'$ and then to $y'=x/3y$
However, Wolfram alpha tells me the answer is $y'=y/x$. Where is my mistake?
No mistake. From your equation, $x^2=3y^2$. So $x/3y$ is the same as $y/x$.