I'm studying some Calculus on my own. I get what appears to be the wrong answer for this one implicit differentiation exercise, and I don't know why.
I have to find $\frac {d^2 y}{dx^2}$ of $y^2-2x = 1-2y$. I calculate
$\frac{dy}{dx} = \frac{1}{1+y}$
and from there I get
$\frac {d^2 y}{dx^2} = \frac{-y'}{(1+y)^2} = -\frac{1}{(1+y)^3}$
Now, Wolfram Alpha tells me I got $f'$ right but $f''$ wrong. It says
$\frac{\delta^2y(x)}{\delta x^2} = - \frac{1}{2(1+x)(1+y)}$
WA hasn't steered me wrong so far. Pointers to where I'm going wrong would be appreciated.