The equation
$x^3 + 2y^3 + z^3 + xyz = 4$
$x,y > 0$ describe a graph of a function: $ z = f(x,y)$.
Find, $\frac{\partial f}{\partial x}$ and $ \frac{\partial^2 f}{\partial x\partial y}$
So I know how to find the first one, you just take the derivative in accordance to x, but I'm confused on how to do the second one.
The second one is probably better notated as follows:
$$\frac{\partial f^2}{\partial x \partial y} = \frac{\partial}{\partial x} \left( \frac{\partial f}{\partial y} \right)$$
In other words, you just find the partial derivative of $f$ with respect to $y$, and then find the partial derivative of that with respect to $x$. The notation is a little unintuitive so I can see the confusion.