Let f(x, y, z) = xyz - xyz^3, find the gradient of f. Enter your answer as an ordered triple (∇f(x, y, z) = a(x, y, z), b(x, y, z), c(x, y, z)).
grad f(x, y, z) = (∂f/∂x, ∂f/∂y, ∂f/∂z)
Evaluate the gradient at the point P(-1, -5, 1). Enter your answer as an ordered triple (∇f(-1, -5, 1) = a, b, c).
grad f(-1, -5, 1) = (∂f/∂x, ∂f/∂y, ∂f/∂z)
Find the rate of change of f at P in the direction of the vector u = (0, 3/5, -4/5).