I am having trouble powering through this question, and I think I just need a nudge in the right direction...
Let the function z = f (x,y) be given implicitly by the equation
$x^{3} + xz = z^{3} + 2yz$
Find the gradient of f (x,y) at the point (2,1)
So far I have found the partials to be..
$\frac{\partial z}{\partial x} = -\frac{3x^{2}+z}{x-3z^{2}-2y}$ and $\frac{\partial z}{\partial y} = -\frac{2z}{x-3z^{2}-2y}$
But I am unsure if those are correct.