Which of the following is the gradient vector of the function f(x, y, z) = cos ry sin yz? Select one: None of them Vf(z., 2) = (-y cos(ry) sinz,- cos(zy) sin z, cos(ry) cos z) f(a.y. =) = (-y sin(ry) sinz,- sin(xy) sin z, cos(zy) cos z) Vf(x.y, z) = (y sin(ry) sin z. a sin(ry) sin z, - cos(ry) cos z) Vf(x,y,z) = (-sin(y) sin z, -r cos(ry) sin z, - cos(ry) cos z)

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: B A' A is the point (3, 1). Bis the point (a, 11). The gradient of AB is 5/½ 7 4

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Q: Find the directional derivative of f(x, y) = x²y³ in at the point (−1, −1) in the direction û given…

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Q: Calculate the gradient of f(x, y) = sin(x² - y) Vf=

A: Finding the partial derivative of the function.

Q: 2. Find the directional derivative of f(x,y) = x cos y in the direction of v = 22, -1). A. (2 cos y…

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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: Let f(x, y) = 10-3r² +4. (a) Find the gradient Vƒ(2,-3) of f at the point P(2,−3). (b) Find the…

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Q: Find the gradient Vf and the directional derivative at the point P (1,–1,2) in the direction a =…

A: The given function f(x, y, z) = x3z - yx2 + z2.The gradient of a function f is defined as∇f(x, y, z)…

Q: Suppose we know that for a function f we have Vf(x, y) = (6x, 6). Find the directional derivative of…

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Q: For z = e"v In(ry): - Find the gradient of z when r= and y = 2 - Find the directional derivative of…

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Q: The gradient of V = x²sin(y)cos(z) at the point (1, 5,0) is إختر أحد الخيارات: 2i + j a O 7+ 25.b O…

A: Given function is  V=x^2 sin(y)cos(z)

Q: 3. Find the directional derivative of f(x, y) = cos(3x+4y) at the point (7/6, π/6) along the…

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Q: If f(x, y, z) = 4zy², then the gradient at the point (5, 2,5) is Vf(5, 2, 5) =

A: Given that, f(x, y, z)=4zy2 Aim: Find ∇f5, 2, 5

Q: Find the directional derivative of f(x, y) = sin(x+2y) at the point (-3, 5) in the direction = π/6.…

A: Given function: We have to find the directional derivative for given function at the point  in the…

Q: 6. Let F(x, y, z)=2xy² + 2yz² + 2x²z. a. Determine the maximum directional derivative of F at the…

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Q: (I) The directional derivative Duf(a, b) is parallel to the vector u. (II) If u is perpendicular to…

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Q: (- 4,3). a) Let f(x, y)= x²y°. Find the directional derivative of f at P(-1,1) in the direction of ū…

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Q: 4) Let f(x, y) = x² – 2xy a) Find the gradient of f at the point (1, –2). b) Use the result of (a)…

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

A: The given function is: f(x,y)=cos(x2y3) So, ∇f(x,y)=∂f∂x,∂f∂y…