Prove that the directional derivative of flay.2) = aysinz. direction v=i +2j+2k 1Is Sin Z at (1,2,7)in the %3D
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Q: directional derivative
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A: Since you have asked more than 3 questions, I am solving first 3 questions. Please repost the other…
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- Suppose ƒ is differentiable at (9, 9), ∇ƒ(9, 9) = ⟨3, 1⟩, and w = (1, -1). Compute the directional derivative of ƒ at ⟨9, 9⟩ in the direction of the vector w.4 Find the directional derivative of f (x,y)= 2x^2 y^2 -3xy at the point (1,-1) in thedirectiona. of vector v =<4,3> and toward the origin.Find the directional derivative of f(x,y,z) at P(2, 1, -1) in the direction from P to Q(-1, 2, 0)
- Let f(x, y) = arctan(xy). Find the unit vector in the direction where the directional derivative of f at (1, 2) is maximum. What is the maximum rate of change at (1, 2)?Find the directional derivative Duf(1, 1), where f(x, y) = x2 + y2 and u is the unit vector at an angle of π/6 from horizontal.A bee was flying upward along the curve that is the intersection of z = x⁴+xy³+12 with the plane x=1. At the point (1,–2,5), itu event off on the tangent line. Where do the bee hit the xz-plane?
- Find the unit vector u along which the rate of change of the function f(x, y) = x 2 + xy3 at the point (2,1) is maximum. What is this maximum rate of change?Let f(x, y, z) = 3ex cos(yz). a) Find the directional derivative of f at P(0, 0, 0) in the direction of vectorv = 2i + j - 2k b) Find the maximum rate of change of f and the direction in which it occurs.) Compute the directional derivative of f(x, y) = x2y at the point (1, 1) in adirection normal to the ellipse x2 + 2y2 = 1 at the point (1, 0).
- Let f ( x , y ) = 2 x − y + x2 + y4. Which (unit) direction vector u MINIMIZES the directional derivative Du(f), at the point (0,0)?What is the largest value that the directional derivative of ƒ(x, y, z) = xyz can have at the point (1, 1, 1)Use Green's theorem to evaluate fxydx+ x3y3dy where C is a triangle with vertices (0,0), C (1, 0) and (1,2) with positive orientation. (b) Compute the directional derivative of the function f(x, y, z) = xy2 + y2z3 + z3x at the point P(4, -2, -1) in the direction of Q(l, 3, 2)