Suppose that $z$ is defined implicitly as a function of $x$ and $y$ by the equation
$$x^2 + y^z − z^3 = 0.$$
Calculate the partial derivatives $∂z/∂x$ and $∂z/∂y$ at $(x, y) = (1, 0)$.
This is what I have so far: I just want to know if I'm right.
$$∂z/dx = -Fx / Fz = -2x / (y - 3z^2) = 2 / (1 - 3z^2)$$
$$∂z/dy = -Fy / Fz = - z / (y - 3z^2) = - z / (1 - 3z^2)$$