3. Calculate the directional derivative of the function f : R³ → R, defined by f(x, y, z) = y²+xz at the point p = (1,2, 2) and in the direction of the vector = (2, -1, 2)

Find the Directional derivative of the function f(x,y, z) = Vx² + y² + z² from point (1,2, –2) in the direction of vector v = (-6,6 ,–3). %3D

2. Calculate the gradient vector Vf of the function f (x, y) = x² – x + y - x²y - 2y2 at the point (2,1) and sketch it on the attached contour plot (you can save the picture, open in photo editor and use drawing tools). Explain in one paragraph (about 200-300 words) the meaning of the gradient vector Vf(2,1), negative gradient vector -Vf(2,1).

Find the directional derivative of the function at the given point in the direction of the vector v. (x, y, z) = x2y + y²z, (2, 7, 9), v - (2,-1, 2) D(2, 7, 9) =

Find the directional derivative of f(x, y, z)=z³x²y at the point (3, 5, 3) in the direction of the vector v = (-4,4,-4).

Find the directional derivative of the function f(x, y) = xy at the point (x, y) = (4, -1) in the direction of the vector 7= 7+ 5j. Dif(4,-1) =

Find the directional derivative of the function f(x, y) = In(x +y°) at the point (2, 3) in the direction of the vector (- 3, 3)

Find the directional derivative of f(x, y, z) = yz + x³ at the point (2, 3, 1) in the direction of a vector making an angle of with Vƒ(2, 3, 1). f(2, 3, 1) =

Find the directional derivative of the function: f(x, y) z² + 4y at the point (0, 0) in the direction of the vector (– 3, 1). You may enter your answer as an expression or as a decimal with at least 4 significant figures. |

Find the directional derivative of the function at the given point in the direction of vector v. f(x, y) = 2 + 6x√y, (4, 16), v = (4, -3) Duf(4,16) =