You will find the directional derivative of z(x, y) = 5x^2 + xy + 3y^2, in the direction (1, -2) at the point (x, y) = (1, 4).
Throughout this question you should use exact values. Note that you can put numbers in the form cos(2), exp(3), ln(4) and so on, and maple can evaluate them exactly.
Enter all vector answers using square brackets, e.g. [2*x,y] or [exp(3),2] etc.
(a) Enter the gradient \nabla z(x, y) = (z_x, z_y) as a function of x and y.
(b) Enter the gradient at the point (x, y) = (1, 4).
(c) Enter the unit vector in the direction (1, -2).
(d) Hence enter the directional derivative of z(x, y) at the point (x, y) = (1, 4) in the direction (1, -2).
