(a) Assume that f : R → R is differentiable. Prove that the directional derivative at x in the direction of a unit vector v is Vf(x) - v. (b) Using part (a), compute the directional derivative of f in the following case: 12 f(r, y, 2) = 1", x= (e, e, 0), v =i+j +k +13 13 13

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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(a) Assume that f : R³ → R is differentiable. Prove that the directional derivative
at x in the direction of a unit vector v is Vf(x) - v.
(b) Using part (a), compute the directional derivative of ƒ in the following case:
3
v = i+ i+ 13
12
4
f(r, y, z) = 1, x= (e, e, 0),
Transcribed Image Text:(a) Assume that f : R³ → R is differentiable. Prove that the directional derivative at x in the direction of a unit vector v is Vf(x) - v. (b) Using part (a), compute the directional derivative of ƒ in the following case: 3 v = i+ i+ 13 12 4 f(r, y, z) = 1, x= (e, e, 0),
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