a) Compute the gradient of the function f(x, y, z) = e*y² . b)Compute the directional derivative Daf (1, 2, 3), where 1 1 2 2 2 c)Let p(t) be a parametric curve with P(7) = (1, 2, 3), (7) = (-2,5, 3). Compute the derivative (fop)(7).

Q: 4. (a) Determine the directional derivative of f(x, y, z) = zety at the point (1, −1, 1) in the…

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Q: a) Find the directional derivative of f(x, y, z) = x²yz + 4xz² at (1, -2, 1) in the direction 2i - j…

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Q: Calculate the gradient vector Vf of the function f(x, y) = x² – x + y- x²y – 2y2 at the point (2,1)…

A: According to the given information, it is required to determine the gradient vector of the given…

Q: 2 Let f(x,y) = x +y ². Which of the following is the minimum directional derivative of the function…

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Q: Find the derivative of the vector function r(t) = ta x (b + tc), where a = (-5, −1, −1), b = (−2,…

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Q: If the gradient of f is Vƒ = z j - yi – 2xzk and the poi f(x, y, z) = 0, find an equation for the…

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Q: Suppose that f(z,y) is differentiable, and suppose that the directional derivative of f at the…

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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: Consider the function f(r, y) = e=² sin( q² + y²) (a) ) Compute the gradient of f. (b) 1 ) Find the…

A: Given fx,y=e-xsinx2+y2

Q: 2. Consider the function f(x, y) = a) Find the directional derivative of f in the direction of the…

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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: a) Find the directional derivative of the function f(x, y, z) = x2 y (2z+1)² at the point P:(1, -1,…

A: This question is related to gradient and it's properties.....

Q: ) Find the directional derivative of the function f(x, y) = sin²(xy) at the point P (2,7) -2i+j √5…

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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 +…

A: We have to find the directional derivative of f(x, y, z)=x2y2z+4xz at (-1, 2, 1) in the direction…

Q: Find the derivative of the vector function r(t) = ta x (b+ tc), where a = (4, -1,5), b = (-3,-3,-1),…

A: Given, the vector function      r(t)=ta×(b+tc),where       a=4,-1, 5, b=-3,-3, -1, and  c=1, 2, 2,…