Compute ƒxz and ƒzz for ƒ(x, y, z) = xyz - x2 z + yz2.

Q: Find work done by the gradient of f(x, y, z) = zexy- 2y2/z  along the path from (1, 2, 4) to (-1, 0,…

A: By Fundamental theorem line integral,we have Where C is curve joining to

Q: Find the gradient of the function at the given point.

A:

Q: Find all the second partial derivatives. f(x, y) = x8y8 + 7x8y fxx(x, y) =  fxy(x, y) =   fyx(x,…

A: Given that          f(x,y) = x8y8 + 7x8y Here we have to find the second partial derivative of…

Q: .    Find work done by the gradient of f(x, y, z) = zexy- 2y2/z  along the path from (1, 2, 4) to…

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Q: How is the linearization of f (x, y) at (a, b) defined?

A: given,          any function fx,y at a,b

Q: Find fzyæ. f (x, y, z) = x°y®°z° + xy° + y°z f zyr ||

A:

Q: Calculate fxxyz for f (x, y, z) = y sin(x + z).

A: We first differentiate the given function with respect to x twice. Then y and z will be treated as…

Q: Calculate fxxyz for f(x, y, z) = y sin(x + z).

A: For a function in several variables, partial derivative with respect to one variable say x can be…

Q: Find fr, fy, and fz. f(r, y, 2) — вуzIn(4ry) fz fy f: =

A:

Q: Could I get help finding all the second order derivatives please?

A: Given

Q: The gradient of f(x,y,z)=xy2z3f(x,y,z)=xy2z3 at the point (1, 1, 1) is

A:

Q: How is the linearization of f(x, y) centered at (a, b) defined?

A: To define linearization of a function f(x,y) at point (a,b).

Q: Find fzyz. f(r, y, z) = x*y³zª + xy" + y°z f zyz

A: Given-  fx,y,z=x4y3z4+xy7+y6z To Find- fzyx

Q: Find f, and fy. f(x, y) = 5x In xy %3D %3D fy =

A: Solution: The objective is to find the partial derivatives

Q: Find the linearization of z = f(x,y) at P(-3, 2) when f(-3, 2) = 2 and f-(-3, 2) = 1, fy(-3, 2) =…

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Q: Compute the partial derivative: f(x, y) = sin(x" –- 3y) fy(0, ) =

A:

Q: Find ( fx fy, fzf xy f yx fxyz f zzx) for the function: f(x, y, z) = xyz + x²y + z³x + x²y?

A: To find the differentiation of the function

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs…

A: Consider the function: fx,y,z=xlnyz Differentiating with respect to “x” then,…

Q: Y : k=0 y' + (2x + 1)y = 0, rrence relation. For k > 0,

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Q: Find fz and fy- f(z, 9) = [" 9eª dt f.(x, y) = f,(x, y) =

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Q: The gradient of f(x, y) = xy at (x, y) = ( – 3, – 2) is %3D

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Q: The gradient of f(x, y) = xy at (x, y) = (2, 3) is

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Q: Find the partial derivative of f/x and f/y f(x,y)=x/x+y

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Q: Compute the partial derivative fa(, 4, 2) of the function f(2,4, 2) = yz' + 2 – 2 vy + * +2 y. O…

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Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy²= 2 (C- cos x) O y…

A: This question is related to differential equations, we will solve it using given information.

Q: Find the gradient of the function f(x, y) = 3x + 5y2 + 1, at the given point      (2, 1)

A: Given equation - f(x,y) = 3x+5y2+1We can write it as - y = 3x+5y2+1Gradient is given by , dydxNow…

Q: Plot the function f(x, y) = x² – y² over the square region bounded by the lines y =x - 2, y =x+ 2, y…

A: Given the function fx,y=x2-y2

Q: Let f (x, y) = 2x³ + 4y³ + 19xy Find D = frx · fyy - fey at the point (2,2)

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Q: Find the linear approximation to f (x, y, z) = 3, -3, – 1): at the point | F(x, y, z) ×

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Q: Find fr, fy, and fz. f(x, Y, z) = 4yz In(6ry) fz = fy = f: =

A: Given: f(x, y, z)=4yz ln(6xy)

Q: Find fzyz. f (x, y, z) = x°y°z° + xy° + y°z %3D 6-

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Q: Find all the second partial derivatives. f(x, y) = x4y − 3x5y2

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Q: Disccus the hatural of the Critical points: f(x,y) = 3xy-x²-y?

A:

Q: Find fyy for f(x, y) = e* In(y).

A: The given function is fx,y=exlny.

Q: Find the linearization of f(x,y) at the indicated point (X0,Yo): f(x,y) = In (x² + y); (1, 1) L(x,y)…

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Q: Find all the second partial derivatives. f(x, y) = xªy – 2x³y² fxx(x, y) = fxy(x, y) = fyx(x, y) =…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: : Find fz for f(x, y, z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

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Q: The gradient of f(x, y) = xy at (x, y) = (3, 1) is

A:

Q: Find the gradient of f(x, y) = 3xty3 + 4x°y® at (1, 2).

A:

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 fz for f(x, y, z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Integrate f(x,y, z) = 2x – 3y² – 2z+3 over the line segment from the origin to (1, 1, 1) and over…

A: A parametric curve is a normal curve where we choose to define the curve`s x and y values in terms…

Q: The gradient of f(x, y) = xy at (x, y) = (3, 3) is

A: Given problem:- Find the gradient of f(x, y) =xy at (x, y) =(3, -3)

Q: Find the linearization of f (x) = xe¯* at a = 0. (Hint: Remember thne product rule.)

A: Given : fx = xe-x2

Q: Consider function f(x, y) = x cos(TxYy) + x³y. .3,

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Q: Calculate fz(2, 3, 1), where f(x, y, z) = xyz.

A: Given,          fx,y,z=xyz

Q: Find f and fy- f (x, y) = 9e dt f (x, y) = %3D fy(x, y) =

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Q: Find f (1, 1) S(x, y) = In( %3D Vx² + y²

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Q: Find the work done by the gradient of ƒ(x, y) = (x + y)2 counterclockwise around the circle x2 + y2…

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