Find the directional derivative of the function f at the

Question

1. For f(x, y) = x³y² + 2xy + sin(xy), compute f_x, f_y, f_xx, f_yy, and f_xy,

2. For f(x, y) = 4x + 3y - xy, answer the following

a. ∇f(2, 1) =

b. Find the directional derivative of the function f at the point (2, 1) in the direction of the vector v^→ = 3i^→ + 4j^→

c. What is the maximum value of the directional derivative of f at the point (2, 1).

3. Find the equation of the plane tangent to the graph of

f(x, y) = 2x³ -y² + xy, at the point (2, -3, 1).