Find the directional derivative of the function at P in the direction of v. f(x, y) = x³ – y³, P(10, 9), v = V2 (i + j) 2

Q: Find the derivative of the function at Po in the direction of u. f(x, y, z) = In(x 2 + 3y 2 + 9z 2),…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find the directional derivative of f(x, y) = (xy)^1/2  at P(6, 6) in the direction from P to Q(9, 2)

A: The directional derivative (D.D) of function f at point P in the direction of vector a is given by,

Q: a) Find directional derivative of the function at P, in the direction of u where f (x, y, z) = x? yz…

A: From the given problem:   fx,y,z=x2yz+4xz2, P01,-2,-1u=2i+j-2k   From the expression of the…

Q: Find the directional derivative of the function at P in the direction of v. V2 (i + j) f(x, y) = x³…

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Q: Find the directional derivative of the function at P in the direction of v. 1 = √₂ (i+j) f(x, y) =…

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Q: Find the derivative of the function at P0 in the direction of u. f(x, y, z) = ln(x 2 + 3y 2 + 9z…

A: For the solution of the problem follow the next step.

Q: Find the directional derivative of the function at P in the direction of v g(x, y) = /x² + y², P(3,…

A: Follow next step

Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

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Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

A: Given function: Formula used:

Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

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Q: Find the directional derivative g(x, y) = √√√x² + y², of the function at P in the direction of v.…

A: solution is given below

Q: b) Find the directional derivative (D.) of the function at P in the direction of PQ f(z, y) = sin 2z…

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Q: Find the directional derivative of the function f(x,y, z) = ry + yz + zr at M(2,1,3) in the…

A: first we find out the partial derivative of given function and solve it . see 2nd step.

Q: Find the directional derivative of the function f(r,y, z) = xry + yz +. zr at M(2, 1,3) in the…

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Q: Find the directional derivative of f(x,y) = x²y at the point P(-5,5) in the direction of v = 3i –…

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Q: Find the directional derivative of the function at P in the direction of v.  f(x,y) = x2y , P(-5,5)…

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Q: Q2 / Find the directional derivative of f(x.y.z) 4xy +5xz2 +6yz2 At the point P(3,1,4) in the…

A: ∂f∂x=4y+5z2∂f∂x=84∂f∂y=4x+6z2∂f∂y=108∂f∂z=10xz+12yz∂f∂z=168Therefore, the gradient is∇f (3, 1, 4)…

Q: Find the directional derivative of the function f(x, Y, z) = 3e" sin(xy) in the direction of v =…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

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Q: Find the directional derivative of the function at P in the direction of v. (x, y) = x3 - y, P(8,…

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Q: Find the directional derivatives of f(x,y,z) = x² y³ – y³z³ + x* in the direction of r = 2i– k, and…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

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Q: Find the directional derivative of the function at P in the direction of v. == P(1, 2), v = -j f(x,…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x3 – y3, P(6,…

A: Solution is given below:

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Here we use the formula, Dvf(x,y)=∇f(x,y).v

Q: Find the directional derivative of the function at point P in the direction of v. h(x, y, z) = xyz,…

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Q: a) Find the derivative of f(x, y, z) = 4zx – xy² – z,at P,(1,0, 2) in the direction of v = 4i – 5j +…

A: Given: The function, fx, y, z=4zx3-xy2-z at P01,0,2 in the direction of v=4i-5j+40k.

Q: Find the directional derivative of the function at point P in the direction of v. h(x, y, z) = xyz,…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

A: Given,            fx,y,z=xy+yz+xz , P8,9,-8 , v=16i+j-kTo find : Find the directional derivative of…

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x³y³, P(4, 3),…

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Q: Find the derivative of the function at Po in the direction of u. f(x, y) = In(-10x - 7y), P o(-4,…

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Q: O Find for the directional derivative of the function at P,in the direction of A where f(x,y, z) =…

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Q: Find the derivative of the function at P.(0,0,0) in the direction of B. f(x, y, z) = 3e* cos yz,…

A: Directional derivative of the function.

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x³y3³, P(10,…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x³ - y°, P(10,…

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Q: Find the directional derivative of the function at P in the direction of v. g(x, y) = Vx2 + y2, P(3,…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x³ - y, P(6,…

A: As we know that; The expression for the directional derivative of the function f in the direction of…

Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

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Q: Find the directional derivative of the function at P in the direction of v. g(x, y) = Vx2 + y2, P(7,…

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Q: Find the derivative of the function at P,(0,0,0) in the direction of B. f(x, y,z) = 3e* cos yz,…

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Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(8,…

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Q: Find the directional derivative of * f (x, y) = 2e* cos y at (0, 7) in the direction of v = (-6, 8)…

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Q: Find the directional derivative of the function at P in the direction of v. V2 f(x, y) = x3 - y3,…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x³ - y³, P(10,…

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Q: 2. For the function f(x,y) = 3x + 4y – xy a) Vf(1,2) = b) Find the directional derivative of f at…

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Q: Use the definition of directional derivative to solve Duf(xo, yo, zo) at point P(xo, yozo) where…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x³ – y³, P(6,…

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Q: Find the directional derivative of f(x,y,z) = x³ + 3xy + 2y + z? at (1,1, 1) in the direction of v =…

A: We will use the fact that the directional derivative of a function at a point in the direction of a…

Q: For function f (x, y) x²+1 Find the directional derivative of f at the point (1,2) in the direction…

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