# Differentiable Manifold

atomqwerty

## Homework Statement

In which points the surface $$\{\left(x,y,z\right)\in\Re^{3}|x^{3}-y^{3}+xyz-xy=0\right\}$$ is a differentiable manifold (subvariedad diferenciable in spanish). Calculate its tangent space in the point (1,1,1).

NA

## The Attempt at a Solution

I've been several problems with the definition of Subvariedad - I don't know if it's said Manifols in english

Thank you

Do they want the tangent space or tangent plane? For the latter, it is just the plane perpendicular to $$\nabla (x^{3}-y^{3}+xyz-xy)$$, fot the former it's slightly more complicated