Let a be a real number and f(x, y) = 4ax?y+ 3xy³. Let v = 3i – j and let Vf(x, y) denote the gradient of f(x, y). i) Find Vf(1,1) in terms of a. -16/5 ii) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is find a.

Q: Find the gradient of the function at the given point. g(x, y) = 3xe/x, (10, 0) Vg(10, 0) = 3i + 3i

A: g(x, y)= 3 x eyx∇g(x, y) =∂g∂x, ∂g∂y∂g∂x=3eyx+3x eyx-yx2      =3eyx 1-yx∂g∂x=3eyx (x-yx)∂g∂y=3x1x…

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A: From the basic vector calculus

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