Let if (x, y, z) # (0,0, 0) if (x, y, z) = (0, 0, 0) xyz x²+y²+z² > f(x, y, z) = { 10, (a) Use the definition to find the directional derivative of the function f at (0,0, 0) in the direction (a, b, c), where a² + b² +c² = 1. (b) Use Lagrange Multipliers to find the maximal and minimal directional derivatives.

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A: The function is given as , fx,y,z=xy-xy2z2 find the directional derivative at point P1,-2,1 in…

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Q: 4. If f(x, y, z) derivative of f at (1,3,0), in the direction of i = i+ 2j – k. = x sin yz, (a) find…

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Q: Q4:- Find the derivative of the function at Po in the direction of the vector AC. f(x, y, z) = x² +…

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Q: a) Compute the directional derivative of the function shown below at the point (1, 0, -2) in the…

A: Since, you have posted multiple question. I am answering first one. Please post again with specific…

Q: Find the Directional derivative of the function f(x,y,z) = /x² + y² + z² from point (1,2, –2) in the…

A: The objective is to compute the directional derivative of the function fx,y,z=x2+y2+z2 from point…

Q: 2y Find the directional derivative of f(x, y, z) = x + z at P(4,4, –3) in the direction from P to…

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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: 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: Given that      f(x,y,z)=ln(x2+3y2+9z2), P0(3,3,3), u=3i+4j Here we have to find the derivative of…

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A: Solved below

Q: Show that the function defined by xy √x²+y² f(x, y) {{ = 0 if (x, y) = (0,0) is not differentiable…

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Q: Let f(x, y, z) = x In y - exz.Calculate the directional derivative of fat point (-5, 1, -2) and…

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Q: Suppose that f(æ, y) f(x, y) in the directional (1, – 1) and at the point = xy. The directional…

A: Here, the given function is: f(x,y)=xy So, ∇f=∂f∂x,∂f∂y⇒∇f=y,x⇒∇f(4,-3)=-3,4

Q: Find the directional derivative of the function f(x, y) = ln(x³ + y³) at the point (3, − 2) in the…

A: Use the gradient of function for finding the directional derivative.

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A: Definition used -          Directional derivative at the point -     The rate of change of f(x, y)…

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Q: 3. At point (1,0,3) on the surface f(x,y) = 2x^2 + 3 y^2+ z^2-11, the directional derivative in the…

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Q: a) Compute the directional derivative of the function shown below at the point (1, 0, -2) in the…

A: The given scalar field is - f(x,y,z)=(x^2)z+(y^3)(z^2)-xyz

Q: Find the directional derivative of F(x , y , z)=7y2e−x+3z2 in the direction u=(3,6,−2) at the point…

A: We have to solve

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Q: Find the directional derivative of f(x, y, z) = xz + y°, at (3, 2, 1) in the direction of 3 = 1+3+…

A: We need to find gradient of f at point (3,2,1)

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Q: Find the maximum value of the directional derivative of the function f(x, y) = tan at the point…

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Q: Find the directional derivative of f(x, y, z) = xy²z³ at P(3, 1, 1) in the direction of Q(0, -5, 7).…

A: Given function: fx,y,z=xy2z3

Q: Find the directional derivative of f(x, y, z) = xy + z 3 at the pointP = (3, -2, -1) in the…

A: fx, y, z=xy+z3,  P=3, -2, -1. Now, ∂f∂x=y·1+0=y∂f∂y=x·1+0=x∂f∂z=0+3z2=3z2 Now, ∇fx, y, z=∂f∂x, ∂f∂y,…

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

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Q: a) If W = F(x ,y),where x =v²-g and y 2vg calculate W +W, %3D b) What is the directional derivative…

A: W=f(x,y) and x= v2-g2 & y=2vg   Wx = dW/dx = (df/dx*dx/dv) + (df/dx*dx/dg) ..............From…

Q: Suppose that f(z, y) = z*y°. The directional derivative of f(1, y) in the directional ( – 1, – 2)…

A: We can solve this as follows:

Q: 10. Let f(x, y) = x² + y³. Calculate the directional derivative of f in the direction of = (4, 3) at…

A: The given function is: f(x,y)=x2+y3Direction vector is:  v→=4, 3Given point:  P=(1, 2)

Q: Find the directional derivative of F(x,y,z)=(xy^2)lnz at (1,2,e) in the direction of

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Q: Let v = (3,4, 12) . Find the directional derivative of f(x,y, z) = x – y² +3z³ in the direction of…

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Q: /Find the directional derivative of the function (f(x, y, z) = x + xcosz-ysinz+y), P₁(0,1,2). at…

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Q: a) Compute the directional derivative of the function shown below at the point (1, 0, -2) in the…

A: NOTE:- As per our guidelines, We’ll answer the first question since the exact one wasn’t specified.…

Q: Find the directional derivative of f(x,y,z)=3xy+z2 at the point (−3,5,5) in the direction of the…

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Q: Find the derivative of f(x, y, z) = x3 - xy2 - z at the point po (2,1,0) in the direction of vector…

A: Given the function fx,y,z=x3-xy2-z at the point p02,1,0 in the direction of vector v=2i-3j+6k. Find…

Q: 6. Find the directional derivative of the function f (x, y, z) = x²z – xyz³ + xyz + y – 1 + z from…

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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: Let f(x,y) = (x² + (G))°. Determine the directional derivative of f at the point (1,0) in the…

A: Explanation of the answer is as follows

Q: Use Green's theorem to evaluate fxydx+ x3y3dy where C is a triangle with vertices (0,0), C (1, 0)…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: What is the directional derivative of f(x,y,z) = ln(x²+2y²+ 4z²) at the point P(-1, 2, 4) in the…

A: The given function is; f(x,y,z)=ln(x2+2y2+4z2) Point P(-1,2,4) u=-3i/13 -4j/13 -12k/13.

Q: If (x, y, z) = cos(x – y)+ e² compute directional derivative of Í at (3, 3, 0) in the direction of ŷ…

A: Option C is correct option.

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