# Existence of directional derivative

For a two variable function, does the existence of continuous partial derivatives of order 1 with respect to $$x$$ and $$y$$ at a point $$(x,y)$$ imply the existence of the directional derivative in any direction at the point $$(x,y)$$?

• Hint: Try defining the derivative with respect to an arbitrary direction, then separate it so it can be derived from the partial derivatives. – Mefitico May 2 at 17:42

1. The continuity of the partial derivatives implies that the function is differentiable at $$(x,y)$$. (This is a standard multi-variable calculus theorem.)