Let w: R³ → R³ be a differentiable vector field, given as w(r, y, z) = (a(x, y, z), b(x, y, z), c(x, y, z)). Fix a point p = R³ and a vector Y. Let a: (-E,E) → R³ be a curve such that a(0) = p. a'(0) = Y. (a) Show that (wo a)'(0) = (Va-Y, Vb - Y, Ve-Y). In particular, (woa)'(0) is independent of the choice of a. Denote this derivative by Dyw(p). (b) Suppose f.g: R³ →R are differentiable functions, Y, ZER are two vectors. Show that D(fY+92)w=fDyw+gDzw.

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