9. (10%) Find the directional derivative of the function f(x, y, z) = x cos y sin z at the point (1, π, π/4) in the direction of the vector 2i-j+4k.

(a) (10%) Then, the function F defined on [a, b] by F(x) =f(t)dt is continuous on [a, b] and differentiable on (a, b). Prove that F'(x) = f(x) for all x in (a, b). Hint: F(x+h)-F(x) f(x) × h if h is small enough. (圖示證明(pictorial proof)即可)