(3 points) the directional derivative of f(x, y) at (2, 1) in the direction going from (2, 1) toward the point (1, 3) is −2/ √ 5, and the directional derivative at (2, 1) in the direction going from (2, 1) toward the point (5, 5) is 1. compute fx(2, 1) and fy(2, 1).

The vector pointing from (2, 1) to (1, 3) points in the same direction as the vector . The derivative of at (2, 1) in the direction of is

We have

Then

The vector pointing from (2, 1) to (5, 5) has the same direction as the vector . The derivative of at (2, 1) in the direction of is

so that

Solving the remaining system gives and .

angle uzt is congruent to angle tzy. angle vzw is congruent to angle yzx.

(credits to leowren)

step-by-step explanation: