F(x, y, z) = (y²z + 2xz2)i + 2xyzj + (xy2 + 2x²z)k, C: x = Vt, y = t + 3, z = t2, 0sts 1 %3D (a) Find a function f such that F = Vf. f(x, у, 2) %3D

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y - 4xyz + 6yz²…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y – 4xyz + 7yz2 s(x,…

A: As we know that the sum/difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 Given:…

Q: Find all the second partial derivatives. f(x, y) = x^y – 3xSy2 fxx(x, y) fyr(x, Y) %3D

A: Given: f(x,y)=x4y-3x5y2

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y – 9xyz + 10yz²…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x3y - 3xyz + 9yz2 %3D…

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Q: Find the partial derivatives of the function f(x, y) = xye²v f-(@, y) = fo(x, y) = %3D fzy(x, y) %3D…

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Q: Find all the second partial derivatives. f(x, y) = x^y – 2x5y² fxx(x, y) fxy(X, y) = fyx(x, y) =…

A: fx, y=x4y-2x5y2 Partially differentiating with respect to x, we get fxx, y=y·4x3-2y2·5x4=4x3y-10x4y2…

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x²y - 5xyz + 7yz?…

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Q: Find the gradient of the function f(x,y,z) = x2 + y3 - 2z + z In x at point P (2, 2,1) %3D

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x2y - 7xyz + 8yz2…

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Q: a. w = √√x² + y² + z² xy b. w = x+y+z c. w = In√√x² + y² + z² 1

A: Use the procedure of partial derivatives to find with respect to x y and z as in next step.

Q: f z = f (x, y) is a function that admits second continuous partial derivatives such that: ∇f (x, y)…

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Q: Suppose X = s“, y = st and z = tu. The function W=f(x,y,z) has the partial derivatives Wx = Wy = Wz…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y – 5xyz + 7yz? %3D…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x-y - 8xyz + 6yz %3D…

A: Given:- f(x, y, z) =3x2y-8xyz+6yz2 To find:- fx(x, y, z), fy(x, y,z), fz(x, y, z)

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y – 9xyz + 8yz2…

A:

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x?y - 4xyz + 8yz? %3!…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y – 2xyz + 9yz2…

A: The solution is given below in the next step:

Q: Suppose X = s“, y = st and z = tu. The function W =f(x,y,z) has the partial derivatives Wx = Wy = Wz…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x?y – 6xyz + 10yz2…

A: Given problem:- Find the first partial derivatives with respect to x, y, and z.   f(x, y, z) = 4x²y…

Q: Suppose X = s, y= st and z = tu. The function W = f(x,y,z) has the partial derivatives Wx = Wy = Wz…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x2y – 4xyz + 6yz2 %3D…

A: We have to find

Q: Use the Chain Rule to evaluate the partial derivative at the point specified. ag at (u, v) = (0, 1),…

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Q: f(x, y) = y + sin(), (0, 5) The partial derivatives are f (x, y) = and f,(x, y) = , so f,(0, 5) = […

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Q: A function f has partial derivatives fx = 4x + y² - 6y +5, fy= 2xy - 6x. (a) Find the stationary…

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Q: Integrate f(x, y) = (x + y + 1)- 2 over the triangle with vertices (0, 0), (4 , 0), and (0, 8).

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the first partial derivatives with respect to x, y, and z. Ex, y, 2) = 3x?y - 6xyz + Byz? ,(X,…

A: We have to solve this problem by partial derivative method.

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x?y – 3xyz + 8yz?…

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Q: Find f, fy, and f. f (r, y, z) = z In (a*y® cos(2z)) f%3= fy = %3D fz =

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y – 5xyz + 10yz?…

A: Topic-partial derivatives

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x2y – 3xyz + 7yz?…

A: Partial derivatives

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4xy – 6xyz + 10yz f,(x,…

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Q: If f(x, y, z) = 2x5 + 3y5- 8x2y?z?, what is the partial derivative of f with %3D respect to z? fz =…

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Q: uppose z = z (x, y) is a function that admits partial derivatives of first order which satisfies the…

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Q: F(x, y, z) = (x, xy²2, xz) Scap: r(u, v) = (u, v, (u² − 1) (v² - 1)), Slevel: Tlevel (u, v) = (u,…

A: As per the question we are given a vector field F along with its divergence i.e. div(F) And a 3d…

Q: Find fz and fy- f(x, y) = Te“ dt f„(x, y) %3D S,(x, y) =| %3D

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Q: Find the first partial derivatives with respect to x, y, and z. F(x, y, z) = 3x y - 8xyz + 7yz2…

A:

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y – 9xyz + 8yz2 syz?…

A: The objective is to find partial derivatives with respect to x, y and z.

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x²y – 6xyz + 10yz? %3D…

A: topic - partial derivatives

Q: Find the first partial derivatives with respect to x, y, and z. 潮期 F(x, y, z) = 4x²y 4x3y- - 8xyz +…

A: see below the answer and explanation

Q: Show that the function x² + y? (x, y) # (0,0) f(x,y) = x - y 0, has partial derivatives f.(0,0),…

A: Given function is fx,y=x2+y2x-y¯    x,y≠0,00      ,   x,y=0,0 Show that the function has partial…

Q: Find the first partial derivatives of the function. f(x, y, z) = xz – 7x3y3z6 fx(x, y, z) fy(x, y,…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y – 5xyz + 9yz?…

A:

Q: Use the Chain Rule to evaluate the partial derivative g at the point (r, 0) = (2/2, 7) where g(x, y)…

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

Q: Find all the second partial derivatives. f(x, y) = x^y – 4x³y? fxx(X, y) = fxy(x, y) = fyx(x, y) =…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y - 9xyz + 6yz²…

A: The objective of the question is determine the partial derivative.

Q: Consider f(x, Y, z) Find all the first order partial derivatives fr, = 2x³ – 2y³ + 4z³ – 72²y?2².…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x y - 9xyz + 10yz %D…

A:

Q: Find all the second partial derivatives. f(x, y) = x5y5 + 4x®y fdx, y) = f(x, v) = fydx, y) = fyy(x,…

A: Given that: f(x,y)=x6y6+4x8y

Q: 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…

A: fx, y , z = xyzx2 + y2 + z2, if (x, y , z) ≠(0,0,0)                             0,…