Find the directional derivative of the function z(x, y) = e³tan(y) + (x + 1)²sin(2y) at the point P(0, 77/4) in the direction of vector a = i + j√3. Present your answer in the exact form (don't use a calculator).

Please don't provide handwritten solution .....

1 (a) Find the point that is a distance 0.1 from the point P = (3,5) in the direction of v = (3,-1). Give five decimal places in your answer. Q = ( (b) Use P and Q to approximate the directional derivative of f(x, y) = √√x+3y at P, in the direction of v. f.≈ (c) Give the exact value for the directional derivative you estimated in part (b). fv

Solve it on paper!