on pages 14-15, in deriving the normal vector to a surface, they use a plane to cut the surface (the plane is parallel to the xz plane) then use the curve 'c' in the xz plane (this curve being where the plane intersects the surface), draw a tangent vector 'u' and want to use the components of 'u'. Now, they use an arbitrary length called 'u sub x' in the x direction (this again is in the xz plane) but WHY is the component in the z direction designated 'partial f/partial x times u sub x'? My question is NOT "why is the derivative of z with respect to x replaced with the partial derivative of f with respect to x", that I understand. But why in the first place is the change in the z direction a derivative times change in x?(adsbygoogle = window.adsbygoogle || []).push({});

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# Question from reading Div Grad Curl and All That

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