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# Quick partial derivatives question watch

1. I've got a quick question: for a function does ?
2. (Original post by Monaa123)
I've got a quick question: for a function does ?
I have very little experience with partial derivatives but I swear I recall in this context. I could be wrong though.
3. (Original post by alex2100x)
I have very little experience with partial derivatives but I swear I recall in this context. I could be wrong though.
It might be? I know that the contours at f = constant have a slope I don't really understand the relationship between contours and derivatives though.
4. Let

Divide through by and let

Our initial statement means that

Thus:

5. (Original post by Phichi)
Let

Divide through by and let

Our initial statement means that

Thus:

Ohh, that makes sense. Thank you!

So the gradient of the plane is the same as the gradient of the contour? But then what is the gradient vector and why is that orthogonal to the contours?
6. So I was going over it. And the line perpendicular to the contour has the slope so to be orthogonal it has to be parallel to but I don't understand how it's parallel? It's probably something really obvious but I just can't see it :/

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Updated: January 8, 2015
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