Find dz dt where Z = 4x cos y and x = t2 y = 2t4 Give your final answer in terms of t. Show all steps in finding the derivative. Simplify.Compute the gradient of the given function f and evaluate it at the point P. Then find the directional derivative of fat P in the direction of u. Use exact values. f (x, y ) = V4 -x2 - 2y at the point P(2, -2) 1 3 U = 10 V10The function f (x, y) = 2x2+ y2 has an absolute maximum and absolute minimum subject to the constraint x2 + 4y + yz = 32 Use Lagrange multipliers to find these values. Solution must include all steps in solving the equations Use exact values