a) Find the directional derivative of the function at the given points in the direction of vector v. h(x, y, z) = cos(xy) + ey² + Inyz, Po(1,0, ¹/2), v = i + 2j+2k. b) Find the local extreme values of f(x,y) = x² + 3xy + 3y² - 6x + 3y - 6. Solution # 5 (to be typed here by the student)

Q: A function z=f(x, y) is defined implicitly by the equation xy2 - x²z+yz² -z = 11 near point (2, -2,…

A: Given function is fx, y, z = xy2-x2z+yz2-z-11

Q: 5. Find the directional derivative of f(x, y) = xy – y at the point (1, 2) along the unit vector…

A: The given function is: f(x,y)=xy-y2 Given point is: P = (1, 2) Direction vector is: v=3, 4

Q: Consider the function Question 1 x f(x, y) = -y ln x + x lny + y a) Find the directional derivative…

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Q: of f(x, y, tion of ve

A:

Q: Determine the directional derivative of f(x, y, z) = tan-1 221) where U = (-1,2,2) at P(0, 1, 1).…

A: The given function is fx,y,z=tan-1xy22z2-1. The direction vector is u=-1,2,2 and the point is…

Q: (d) Let f(x, y) = 2x² + xy-y². Prove that the directional derivative of f(x, y) at point x = (3,-2)…

A:

Q: 5. Find the directional derivative of f(x, y) = y² + (x²/y), at the point (2, 1) in the direction of…

A:

Q: Find the directional derivative of the function f(x,y,z) = tan (xýz) At point (1,2,3) İin the…

A: The solution is given as

Q: You are given the derivative of a vector function r in the component form is dr (e,3e",-2t). You are…

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A:

Q: #3. Consider the function xy2 if (x, y)# (0,0), f (x, y) = {x2+y2 if (x, y) = (0,0). Calculate the…

A: Given function is fx,y=xy2x2+y2if x,y≠0,00          if x,y=0,0 We have to calculate the directional…

Q: The directional derivative of f(x, y) = cos(x²y³ ) in the direction of the vecto v = 3i + 4j is Du…

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Q: Q3 Find the directional derivative of f(x,y,z)=xy+yz+zx at the point (1,-1,2) in the direction of A…

A:

Q: Prove that the directional derivative of f(x, y) = y + 2xy³+x²y2 at point (0, 1) in the direction…

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Q: Find the directional derivative of f(x, y, z) = x²y²z + 4xz at (-1,2,1) in the direction 2i + j +…

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Q: The directional derivative of f(x, y, z) = xyz at point (-1, 1, 3) in the direction of vector î - 2ĵ…

A: Remark: We know that the directional gives the rate of change of a function at a specific point in…

Q: Let f(x, y) = x²y + y²x. Find the directional derivative at (-3, 2) in the direction = π/2.…

A: