Let be a subset of be a function, be an interior point of , and let be a vector in . I want to show if is differentiable at , then is also differentiable in the direction at , and where Thanks
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What is your definition of 1) Differentiable 2) Differentiable in the direrction v?
Originally Posted by HallsofIvy What is your definition of 1) Differentiable 2) Differentiable in the direrction v? I say is differentiable at with derivative if we have where is the lenght of as measured in the metric I say is differentiable in the direction at if the limit exists.
Originally Posted by bram kierkels I say is differentiable at with derivative if we have where is the length of as measured in the metric I say is differentiable in the direction at if the limit exists. So what happens if you put in the first of those definitions?
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