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 $y''(1)=0$)

$$x^4+y^4=2.$$ 
$$y^4=2-x^4$$
On differentiating with respect to $x$, we have
$$4y^3y'=-4x^3$$
$$y^3y'=-x^3$$
Again differentiating with respect to $x$, we have
$$3y^2(y')^2+y^3y''=-3x^2$$
Now Put your conditions and get your answer.
