# Unit normal vector to the curve of a function at a point

How can I derive the formula for the normal unit-vector to the curve of a function at a given point $p$?

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If curve is represented by $f(x,y)=0$, then $\nabla f_{(x_0,y_0)}$ is normal vector to curve at point $(x_0,y_0)$
What's the name for that reflected $\Delta$? – saadtaame Mar 7 '13 at 19:29