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 (xo,yo,zo)are just the tangent lines at (xo,yo,zo) along the planes y=yo and x=xo. Directional derivatives were explained to be derivatives at a particular direction defined by the unit vector a→=cos∅xλ sin∅yλand it is given by Daf(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.