Let F(x, y) = [2ry² +x, 2r²y + y]. Find all functions f with gradient F. Find the derivative of f in the direction of [2, 1] at the point (3,3). At the point (3,3) in which direction is the directional derivative of f maximal? What is the value of the direc- tional derivative of f in this direction at (3,3)? Find the equation of the tangent plane to z = In(2r + y) at (-1,3).

Q: Find the gradient of the function z = cos(x2 + y2), at the given point (3, −4)

A: Given=z=cos x2+y2 at point x,y=3,-4Gradient∇x,y=fxx,yi+fyx,yjwhere fx,y=z=cos x2+y2

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

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Q: let f(x,y,z)=ax3y + by2e1-z+cze1+z be a function . Find a, b, c, so that the maximum value of the…

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Q: Find the gradient of the function f(x, y, z) = yz², at the point (0, -1,–1) V f(0, –1, –1) =

A: fx, y, z=yz2 & the point is 0, -1, -1. Partially differentiating with respect to x, we get fxx,…

Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

A: The given function is g(x,y)=lnx2+y23 We have to find the gradient of the function and maximum value…

Q: Find the gradient of the function f(x, y, z) = xeyz, and the maximum value of the directional…

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Q: If the gradient of f(x, y, z) at (1, 2, 3) is 2i – 2j +k, then the maximum value for a directional…

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Q: Find the gradient of the function at the given point. Function Point f(x, у, 2) : x2 + y2 + z? (7,…

A: Formula for the directional derivative of the function f(x,y,z) is: ∇f = fxi +fyj +fzk Where…

Q: Use the gradient to find the directional derivative of the function at P in the direction of Q. f(x,…

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Q: Use the gradient to find the directional derivative of the function at P in the direction PQ. f(x,…

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Q: Find the maximal value of the directional derivative of w = xy°z at the point (2, 1, 1)

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (19, 5, -1) Vw(19, 5, -1) =

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Q: Choose the gradient of the function f defined by f(x,v,z) = cos(xy +9xz + 13yz). O sin(xy O -cos(…

A: Take gradient and solve

Q: Find the gradient of f(x,y.z)= (x2 + y2 + z2) - 1/2 + In (xyz) at the point (1,- 2, - 2) %3D Vf (1.…

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Q: Let f(x, y) = exy and P(1, 0). Solve for the gradient of f at the point P.

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Q: Which of the following is the gradient vector of the function f(x, y) = 3x ln 3y - 2x²y at point (1,…

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Q: Let f(x, y, z) = xy² 23 Find the directional derivative of the function at the point (1,-2,1) in the…

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Q: The gradient of f(æ, y) = e3 * sin(2 · y) at (2, y) = (3, – 2) is defined as followed: V f(æ, y) =…

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Q: A particle moves in a plane according to -t, x = (t+1)e; y=2tet -t Determine the simplified…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of Q. f(x,…

A: We know that the directional derivative of a function f(x, y) at a point P in the direction of a…

Q: Use the gradient to find the directional derivative of the function at P in the direction of  PQ.…

A: This is question of application of differentiation which we will proceed as follows

Q: Find the gradient of the function f(x, y, z) = √(x2 + y2 + z2), and the maximum value of the…

A: The given function is fx,y,z=x2+y2+z2

Q: Let f(x, y, z) = x In y - exz.Calculate the directional derivative of fat point (-5, 1, -2) and…

A: In this question, we find the directional derivative of the function f(x,y,z)=xln(y)-exz3The line…

Q: Compute the gradient of the function at the given point. f (x, y, z) = In(x² + 7y – 3z²) ; (7,7,7) O…

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Q: Calculate the gradient of f(x, y) xy at (r, y) = (- 3, – 2). %3| V f(– 3, – 2)

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Q: Compute the directional derivative of the function f(x,y, z) = 3ryz at the point P: (1, –3, –1) in…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of Q f(x,…

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Q: Find the direction derivative of f(x,y)= Xe ² + y ² at the paint (2,1), by the dirction of V = i- j

A: Topic:- application of derivatives

Q: Find the gradient of the function f(x, y) = 3x + 5y2 + 1, at the given point      (2, 1)

A: Given equation - f(x,y) = 3x+5y2+1We can write it as - y = 3x+5y2+1Gradient is given by , dydxNow…

Q: Find the gradient of f(x,y,z) = (x² + y² +z²) ¯ - 1/2 Vf(-21.-2)=(1+Dj+k (Type integers or…

A: topic - gradient of a function

Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

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Q: Find the gradient of the function w = 1/(√1 − x2 − y2 − z2),  and the maximum value of the…

A: The given vector is:

Q: Let f(x, y, z) = 3xy + 2yz - xz. Find the directional derivative of f(x, y, z) in the direction of…

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Q: a) If W = F(x ,y),where x =v²-g and y 2vg calculate W +W, %3D b) What is the directional derivative…

A: W=f(x,y) and x= v2-g2 & y=2vg   Wx = dW/dx = (df/dx*dx/dv) + (df/dx*dx/dg) ..............From…

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

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Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

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Q: What is the gradient of f(x, y, z) = x³z2 + y³z +125z - 1 at P(5,5,-1) ?

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Q: 3. Let f(x, y) = In 2x + 4y, find the directional derivative of f(x, y) in the direction of at the…

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Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

A: The solution is given as

Q: Find the directional derivative of f (x, y, z) = xy²z³ at P(2,1,1) in the direction of Q(0,–3,5)

A: Solution: The objective is to find the directional derivative of the given function

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

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Q: Consider the paraboloid f(x.y) = 9--r and the point P(12,0) on the level curve f(x.y) = 0. Compute…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

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Q: Compute the gradient for the function f (x, y) = 4x² – 9y at the point (10, -9) %3D

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Q: Vhat is the gradient of g(x.y) = ye* and its maximum value of its directional derivative at P(0, 5)?…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A: Given that, the function is gx,y,z=xye8z and the points are P3,12,0 and Q0,0,0.…

Q: Find the gradient of the function w = 6xy − y2 + 2xyz3, at the given point  (−1,  5, −1)

A: To find the gradient, take the derivative of the function with respect to x,y,z.