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- 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.Compute the directional derivative of g(x,y)=sin(pi(5x-5y)) at point P(1,-3) in the direction (15/17, 8/17). Be sure to use a unit vector for the direction vector.Find the directional derivative of f(x,y,z)=yz+x^4 at the point (1,3,2) in the direction of a vector making an angle of 5π/6 with ∇f(1,3,2).
- 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>.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.Find a vector equation for the tangent line to the curve of intersection of the cylinders x2+y2=25 and y2+z2=20 at the point (3, 4, 2).
- Find the directional derivative of f(x, y) = 10 − 3x^2 + (y^4)/4 at P(2, −3) in the direction of the vector 〈√3 , −1〉.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 the function at the given point in the direction of the vector u
- Find the directional derivative of f(x,y,z)=yz+x^4 at the point (1,2,3) in the direction of a vector making an angle of pi/6 with f(1,2,3). Fu=?Suppose L(5, 4) was reflected across the line y = x then translated along the vector <4, 0>. What is the y-coordinate of L''?What is special about the derivatives of vector functions of constant length? Give an example.