Consider the following equation. f(x, y) = sin(2x + 5y), p(−5, 2), u = 1 2 3 i − j (a) find the gradient of f. ∇f(x, y) = (b) evaluate the gradient at the point p. ∇f(−5, 2) = (c) find the rate of change of f at p in the direction of the vector u. duf(−5, 2) =

a. The gradient of is simply the vector of its partial derivatives:

b. Compute the value of the gradient at and :

c. The directional derivative of at (-5, 2) in the direction of a vector is

It's not entirely clear what the given vector is supposed to be... I'll consider a more general vector,

Then the derivative of at in the direction of is

both equations and proportions are better.