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- Ex.: Find the directional derivative of the function f(x, y) = x'y* + x*y* at the point (1,1) in the direction of the vector (4,3).Consider the function f(x, y) = y ln x - x ln y - . a Find the directional derivative of f at the point (1, 2) in the direction of the vector v = (-√3, 1). In which direction does f have the maximum rate of change, and b) what is this maximum rate of change?Evaluate along the curve y=x2 from (-1,1) to (2,4). First find the vector valued function r(t) defining the curve.
- Find the direction in which the maximum rate of change occurs for the function f(x, y) 2x sin(ry) at the point (5,3). Give your answer as a unit vector.Let f(x, y) = arctan(xy). Find the unit vector in the direction where the directional derivative of f at (1, 2) is maximum. What is the maximum rate of change at (1, 2)?Find the gradient field of the function g(x,y,z) = 8xy + 6yz + 8xz. Vg= (Type your answer in terms of i, j, and k.) Please solve