Directional derivative Definition and 103 Threads

The question asks: Find the directional derivative of f (x, y, z) = z ln (x/y) at (1, 1, 2) toward the point (2, 2, 1). What I did was find the distance between the two points to be the directional vector (i+j-k) and then I took the norm of the direction vector. so my unit vector =...

"directional derivative" - conventions Warning: nitpicking notational issues ahead! :eek: So the "directional derivative" in vector analysis - the differential rate of increase of a scalar function φ in a vector direction - is by convention* defined starting from the vector gradient (the...

Im reading over about the directional derivative. Stewart, page 800 says: "Proof: If we define a function g of the single variable h by g(h) = f(x_0 + ha, y_0 + hb) then by the definition of a derivative we have g'(0)= lim_{h \rightarrow 0} \frac{g(h) - g(0)}{h} = lim_{h...