Multivariable Functions - Second Derivative Problem So here is the problem:

Calculate the second class derivative on $(1,1)$ of the equation $x^4+y^4=2$

I found this problem on my proffesor's notes. However it doesn't state whether a partial or a total derivative must be calculated. My guess would be the total.
So my approach would be:
1) Name a function $F(x,y)=0$
2) differentiate F to find $y'=\frac{dy}{dx}$
3) differentiate the result again
4) Solve $y'$ for $x=1$
5) Solve $y''$ for $x=1, y'(1)$
Is this approach at any point correct? I'm totally sure there is something that I'm missing. 
(my approach results in $y''(1)=0$)

we have $x^4+y^4=2$ we assume the the derivative exists and we get $$4x^3+4y^3y'=0$$ divided by $4$ we get $$x^3+y^3y'=0$$ and the same thing again:
$3x^2+3y^2(y')^2+y^3y''=0$ with $$y'=-\frac{x^3}{y^3}$$ you will get an equation for $$y''$$ allone.
