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- Obtain the directional derivative of f (x, y) = 2root (x) -y ^ 3 at the point (1,3) in the direction towards the point (3,1), select the correct option.Find the directional derivative of f(xyz)=xy2z3at p(2,1,1)in direction Q(0,-3,5)Find the directional derivatives of Ø = x2yz + 4xz2 at ( 1, -2, -1) in direction 2ax – ay – 2az.
- Find the directional derivative at point A(1,2) in the direction of u=<3,-4>What is the directional derivative of the function at the point (1, 0) in the direction of the point (0,1)The directional derivative of a function in the direction of ⟨3,4⟩ at the point (1,2) is 1df/dx at the point (1,2) is equal to 5/2.Find the directional derivative in the direction of ⟨3, −4⟩ at the point (1,2)
- The force on a particle is described by 8x3 - 6 at a point x along the axis. What is the work done in moving the particle from the origin to x = 5.Explain how a directional derivative is formed from the two partial derivatives ƒx and ƒy.Find the rate of change of the function f(x, y,z) =x^2y + 3xz - 5yz^3 + π,at the point (1, -1,1 ) in the direction pointing towa rds the point (-3,6, 5).
- Use partial derivatives to find the coordinates which give the shortest distance from the point (2,0,0) to the plane 3x+2y-z=2. Confirm that the point is the shortest distance with use of second derivativesA curve C in the plane passes through (0,7) and (5,8). At each point on C, the tangent line has a slope that is proportional to the second coordinate of the point. What is the value of the constant of proportionality?Find the first and second order derivative w=3z7-7z3+21z2