Let f, g and h be real-valued functions of two real variables satisfying the following conditions: f(1, 2) = 3, f_x(1, 2) = -4, f_y = (1, 2) = 2; g (1, 2) = 1, g_x(1, 2) = -1, g_y(1, 2) = 0; h(1, 2) = 4, h_x(1, 2) = -3, h_y(1, 2) = 5. If F(x, y): = f(g(x, y), -y), find (a) (nabla F) (1, 2); (b) The directional derivative of F at (1, 2) in the direction of the vector v = (3, 4).
Show transcribed image text Let f, g and h be real-valued functions of two real variables satisfying the following conditions: f(1, 2) = 3, f_x(1, 2) = -4, f_y = (1, 2) = 2; g (1, 2) = 1, g_x(1, 2) = -1, g_y(1, 2) = 0; h(1, 2) = 4, h_x(1, 2) = -3, h_y(1, 2) = 5. If F(x, y): = f(g(x, y), -y), find (a) (nabla F) (1, 2); (b) The directional derivative of F at (1, 2) in the direction of the vector v = (3, 4).