Originally Posted by

**matt.qmar** Hi,

Given $\displaystyle F(x,y) = 0$, show that

$\displaystyle \frac{\delta^2y}{\delta x^2} = -\frac{F_{xx}F_{y}^2 - 2F_{xy}F_{x}F_{y} + F_{yy}F_{x}^2}{F_{y}^3}$.

So what I think is going on is that when we write $\displaystyle \frac{\delta^2y}{\delta x^2} $ we are assuming we can have y as a function of x, ie $\displaystyle y = \phi(x)$? So, we can also have $\displaystyle F(x,\phi(x))$ which is subject to $\displaystyle F(x, \phi(x)) = 0$. To be honest, I am not sure how to start this problem or how the relationship of all those partials has anything to do with $\displaystyle \frac{\delta^2y}{\delta x^2} $.

Any help much appreciated, thanks!!