Suppose that is differentiable at . Prove that for every , exists and is equal to

My work:

Let , then there exists an open set such that . Let

Find such that

Pick such that

Then there exists such that and

Am I doing this right so far? Thanks.

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- Nov 22nd 2008, 06:13 AMtttcomraderExistence of Directional Derivative for an interior point
Suppose that is differentiable at . Prove that for every , exists and is equal to

My work:

Let , then there exists an open set such that . Let

Find such that

Pick such that

Then there exists such that and

Am I doing this right so far? Thanks.