(adsbygoogle = window.adsbygoogle || []).push({}); Directional and partial derivatives help please!!

I have read that the partial derivative of a function z=f(x,y) :∂z/∂x, ∂z/∂y at the point (x_{o},y_{o},z_{o})are just the tangent lines at (x_{o},y_{o},z_{o}) along the planes y=y_{o}and x=x_{o}. Directional derivatives were explained to be derivatives at a particular direction defined by the unit vector a^{→}=cos∅x^{λ}sin∅y^{λ}and it is given by D_{a}f(x,y)=

∂z/∂xcos∅ + ∂z/∂ysin∅. Partial derivatives were also said to be special cases of directional derivatives when ∅=0° or 90°.

What confuses me is that if ∅=180° or 270°,the directional derivative equals the negative of the partial derivative. The angle was just increasedby 180 so the tangent line remains at the same plane and i think should it not change its value, it is still the same tangent line as before.

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# Directional and partial derivatives help please

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