Question 5 Find the directional derivative off at P in the direction of a. f(x, y,...
Chapter 13, Section 13.6, Question 015 Find the directional derivative off at P in the direction of a. f (x, y, z) = xy + z2; P(3,0,2); a =i+j+k Duf = ? Edit
Find the directional derivative of f at p in the direction of a. f(x,y,z)=xy+z^2; P(2,-2,2);A=i+j+k
Question 6 20x Find the directional derivative of f (x, y) = at P (4,0) in the direction of Q(1, -2). x+y Enter the exact answer. Duf = Edit
Find the directional derivative off at P in the direction of the vector U f(x,y,z) = x²lny P(5,1); U = wait à 1 = ( )
5. Find the directional derivative of the function at Pin the direction of u: a f( -2..2 f(x,y,z) = x2 + 2y2 - 3z-, P.(1,1,1), u = i +j+k.
Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = xyz, (4,2, 8), v = (-1, -2, 2) Duf(4, 2, 8) = -4 X
s (ls points) 1/ Given f(x,>)-xy+e" sin y and P(1,0) a) Find the directional derivative of fat P in the direction of Q(2, 5). b) Find the directions in which the function increases and decreases most rapidly atP e) Find the maximum value of the directional derivative of fat P. d) Is there a direction u in which the directional derivative o f fat P equals 1? If there is, find u. If there is no such direction, explain. e)...
The second directional derivative off(,y) is D2uf(x,y) = Du[Duf(x,y)] Iff(x, y)=x3+ 5x2y4yand ( ), calculate D21,f(2,1) 3 4 The second directional derivative off(,y) is D2uf(x,y) = Du[Duf(x,y)] Iff(x, y)=x3+ 5x2y4yand ( ), calculate D21,f(2,1) 3 4
(5 points) (a): Find the directional derivative of \(f(x, y)=y^{2} \ln x\) at \(P(1,4)\) in the direction of \(\mathbf{u}=-3 \mathbf{i}+3 \mathbf{j}\)(b): Find the equation for the tangent plane and normal line to the surface \(\cos (\pi x)-x^{2} y+e^{x z}+y z=4\) at \(P(0,1,2)\)
Find the directional derivative of f(x,y,z)=xy+z^3 at the point (2,3,1) in the direction of a vector making an angle of 3π/4 with ∇f(2,3,1).