(a) If u (a, b) is a unit vector and f has continuous second partial derivatives, show that D u 2 f f xx a 2 2f xy ab f yy b 2 (b) Find the second directional derivative of f (x, y) xe 2y in the direction of v (4, 6)

Question: (a) If u = (a, b) is a unit vector and f has continuous second partial derivatives, show that D u 2 f = f

(a) If u = (a, b) is a unit vector and f has continuous second partial derivatives, show that D_u² f = f_xxa² + 2f_xyab + f_yyb²
(b) Find the second directional derivative of f (x, y) = xe^2y in the direction of v = (4, 6).

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a From Equation 9 we have Du Vu x fy a b a fb and from Exercise 39 we ... View full answer

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