Directional derivative Definition and 103 Threads

In mathematics, the directional derivative of a multivariate differentiable function along a given vector v at a given point x intuitively represents the instantaneous rate of change of the function, moving through x with a velocity specified by v. It therefore generalizes the notion of a partial derivative, in which the rate of change is taken along one of the curvilinear coordinate curves, all other coordinates being constant.
The directional derivative is a special case of the Gateaux derivative.

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  1. M

    Calc 3 directional derivative question

    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 =...
  2. R

    Directional derivative - conventions

    "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...
  3. Cyrus

    Is the Use of h Confusing in the Directional Derivative Proof?

    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...
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