The directional derivative of f(x; y) at (x0; y0) along u is the pointwise rate of change of f with respect to the distance along the line parallel to u passing through (x0; y0).

S PROFESSOR RICHARD BROWN Synopsis. Today, we move into directional derivatives, a generalization of a partial deriva-tive where we look for how a function is changing at a point in.

This enables us to calculate the directional derivative in an arbitrary direc-tion, by taking the dot product of ∇f with a unit vector, ~u, in the desired direction.

Directional Derivatives Directional Derivatives We know we can write The partial derivatives measure the rate of change of the function at a point in the direction of the x-axis or y-axis. What about the …

Calculate the directional derivative of T(p,V) at the point (p,V) = (1,1) into the direction v = (1,2). We have Tp(p,V) = (3V − 1)/8 and TV(p,V ) = 3p/8 − (9/8)1/V2 − 3/(4V3).

Costello, Schweitzer Engineering Laboratories, Inc. Abstract—Phase and ground directional elements are relied on for fa. t and secure protection throughout the power system. Although directional relays …

For each of the following, determine the maximum value of the directional derivative at the given point as well as a unit vector in the direction in which the maximum value occurs.