7) Find the derivative of the function at P.(-7.-8) in the direction of ū= 121 -...
7) Find the derivative of the function at P. (-7,-8) in the direction of ū= 12i – 5j for f(x,y) = tan-1 -4633)
7) Find the derivative of the function at Po(-7,-8) in the direction of u = 121 – 5j for f(x,y) = tan-- (30)
Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the f(x, y) = P(2,0) @=- 8x + y 6
Find the derivative of the function at P, in the direction of A. f(x,y,z) = xy + y2 + zx, (-2,2,1), A = 91 + 6j - 2k (PAD) (-2,2,1)= (Simplify your answer.)
1. Find the directional derivative of the function f(x, y, z) = 2.cy – yz at the point (1,-1,1) in the direction of ū= (1,2,3). Is there a direction û in which f(x, y, z) has a directional derivative Dof = -3 at the point (1,-1,1)?
6. For a given function f(x, y), is noted that at the point P(1,1) the directional derivative in the direction towards (0,0) is 1, while the directional derivative towards (1.2) is -1. Find andf at 6. For a given function f(x, y), is noted that at the point P(1,1) the directional derivative in the direction towards (0,0) is 1, while the directional derivative towards (1.2) is -1. Find andf at
Vectors: Using the direction -9i -5j and the point (6, -3), find the derivative of the function f(x) = -4xy-8y^2
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
Find the directional derivative of the function f(x,y,z) = z4−x3y2 at P(1,-1,1) in the direction of the vector from P(1,-1,1) to the point Q(2,1,0). What is the maximum rate of change of f at the point P(1,-1,1) and in which direction
3. Find the gradient ãf and the directional derivative at the point P(1,-1,2) in the direction a = (2,-1,1) for the function f(x, y, z) = xºz-yx + 2. In which direction is the directional derivative at P decreasing most rapidly and what is its value?