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- Find the directional derivative of f(x, y, z) = 23x²y at the point (5, -5, 5) in the direction of the vector v = (3,4,-2).Find the directional derivative of f(x,y,z) = z3-x2y at the point (4, -3, 4) in the direction of the vector v = <-1,-3,-2>.Find the derivative of the vector functionr(t)=ta×(b+tc) wherea=⟨−4,−3,5⟩ b=⟨−1,2,5⟩ and c=⟨−3,−2,−3⟩
- 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) = 1+5x/ỹ at the point (5, 1) in the direction of the vector =.Find the directional derivative of g(a, b) = cos(3a + 4b) at the π point ( along the direction of the vector (-4,-3)
- Evaluate the directional derivative Duf (2, 3) if ƒ (x,y) and T2 - y u is the unit vector in the same direction as (-3, 4).Calculate the directional derivative of g(x, y, z) = z² - xy + 4y2 in the direction v = (1,-4, 3) at the point P = (3, 1, -9). Remember to use a unit vector in directional derivative computation. (Use symbolic notation and fractions where needed.) Dvg(3, 1,-9) =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)=xe'+ye² at (0,0,0) in the direction of the vector (-29,2,-17).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) = Vxy at the point P = (2,8) in the direction of the point Q = (5, 4). + Careful: (5, 4) is NOT a vector. It's the point you are moving towards.