How do we find the Gradient Vector?

How do we find the Gradient Vector?



Delta f(x, y) = (df/dx, df/dy)

The Gradient Vector evaluated at a point on the implicit curve f(x, y) = 0 is perpendicular to...?
The Tangent Vector of the curve at that point. This vector is also called the Normal Vector to the curve.

In addition, since the gradient points uphill, it indicates the direction of the f(x, y) > 0 region.

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