Q/ Find the directional derivatives of the function f(x,y,z)= xy+xz+yz at Po(1,1,2)in the direction of v = 2i + j - 2k

Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = P(1, 4, 8),…

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Q: Find the directional derivative of the function at in the direction of A where g(x, y, z)=3excosyz…

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Q: The maximum directional derivative of f (x, y, z) =r sin(zy)-yz + 10 %3D at (1, -1, 0) is O v3 O 2…

A: For the scalar function f(x,y,z), gradient is the maximum rate of change.  So, first we will find…

Q: (a) Find the directional derivative of f (x,y) = In(xy) at (-) in the direction of (1,1).

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

Q: Calculate the directional derivative of the function f(x, y, z) = 2x³y − ln(y)x²z − z² at the…

A: Answer

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

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Q: 4. Determine the directional derivative of f(r, y, z) = xe"+rsinz+a²y at the point (2,0, ) in the…

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Q: Calculate the directional derivative of g(r, y, z) = 4 In(r + e2) at (0, 1, 0) in the direction from…

A: For directional derivative let us first compute derivatives

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: Find the directional derivative of f(r,y, z) = e² cos(Tyz) at (0, 1, ) in 2-1 -y-1= I-2 the…

A: To Find: Directional derivative

Q: Consider the function z = f(x, y) = x° + x² cos y What is the directional derivative at (1,0)) if…

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Q: Find the directional derivative of the function f(x, y, z) = ryz in the direction normal to the…

A: We havefx,y,z=xyz

Q: The directional derivative of the function f (x, y, z) = x²z + xyz + y² in the direction of u = 2i +…

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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 f(x, y, z) = x²y + y²z v = at P(1,2,3) in the direction of %3|

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

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 if f (x, y, z) = 3e* cos(yz) at point %3D (0, 0, 0)…

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Q: Compute for the directional derivative of f (x,y,z) = tan (ax – 2ny)e4y-z at the point (,0, ln 4) in…

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Q: 5. Compute the directional derivative and gradient of f(x, y, z) = 4x – y²e3xz at (2, – 1, 0) in the…

A: Gradient of vector function For a given vector f(x, y, z) the gradient vector denoted by ∇(f) is […

Q: Determine the directional derivative of f(x, y, z) = xe³+xsinz+x²y at the point (2,0,4) in the…

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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 linear approximation to f(x, y, z) = " at the point (2, -1,1): f(x, y, z) z

A: Given the function

Q: Find the directional derivative of the scalar function of (x, y, z) = xyz in the direction of the…

A: Given surface is z=xy

Q: Find the directional derivative D,f(P) of f(x, y, z)= cosx+y+z°-5 at P:(, 1, 1) in the direction of…

A: Solved below

Q: Find the gradient of the function f(x,y,z)=2xe^(y/3)sin(3z). grad f=

A: Given f(x,y,z)=2xe(y/3)sin(3z) We need to find gradient of f(x,y,z)

Q: Compute the directional derivative of f(r.y) = at the point (1, 1) in a direction normal to the…

A: Given that: f(x,y)=x2y at the point (1,1) Ellipse: x2+2y2=1 at the point (1,0)

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 directional derivative of the scalar function of (x, y, z) = xyz in the direction of the…

A: What is Gradient of a Scalar Function: The gradient of a scalar function is vector quantity. It is…

Q: 2. Prove that the directional derivative of f(x, y, 2) = ry sin z at (1,2, ) in the direction v = i+…

A: Given:        fx,y,z=xy sinz         x,y,z=1,2,π2    direction v=i+2j+2k   Differentiate the…

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 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 derivative of the function at Po in the direction of A f(x,y,z) = 3 e* cos (yz), Po(0,0,0),…

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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: 4. Compute the directional derivative of f(r, y) = at the point (1, 1) in a direction normal to the…

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Q: 5. Compute the directional derivative and gradient of f(x,y,z) = 4x – y²e3xz at (2. –1.0) in the…

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Q: Find the directional derivative of the function at the point in the direction given. f (x, y, z) =…

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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: (b)Find the directional derivative of f(x,y,z) = x²y- yz3 + z %3D at point (1,-2,0) in the direction…

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Q: 11. Calculate the directional derivative of the function f(, y, z) = xyz at the point a (-1,0,2) in…

A: See the answer below

Q: Find the directional derivative of f(x, y, z) = xy² + yz% at P(1, – 1, 1) in the direction of a = i…

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Q: ) Compute the directional derivative of f(x, y) = x2 y at the point (1, 1) in a direction normal to…

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Q: Find the linear approximation to f(x, y, z) = " at the point (2, –1, 1): f(x, y, z) =

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: (a) Find the gradient of (x, y, z) = x'yz? at the point P(-2,0, 1). Hence find the directional…

A: Please refer the attached image for complete solution. THANK YOU. NOTE: As  per Bartleby guidlines I…

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: Find the directional derivative of f(x, y, z) = xy²z³ at P(4, 1, 1) in the direction of Q(0, –7, 9).…

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Q: find the derivative of the function at P0 in the direction of u. 1.g(x, y, z) = 3ex cos yz, P0(0, 0,…

A: (Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Ctiofnal g(x, y) = V x² + y², _P(5, 12), v = 3i – 4j -

A: The partial derivatives of f at point (x,y)=(5,12) are :…

Q: Find the gradient of the function f(x, y) = (x + y)/(y + 1),and the maximum value of the directional…

A: Given: fx,y=x+yy+1 The gradient of fx,y can be calculated as, ∇fx,y=i^∂∂xfx,y+j^∂∂yfx,y Here,…

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

A: To find the directional derivative of the function at P in the direction of v.fx, y, z=xy+yz+xz, P1,…

Q: 1. Find the directional derivative of the function f(x, y, z) = 3e" sin(ry) in the direction of v =…

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