twice differentiable

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y - 5xyz + 10yz²…

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Q: Find the first partial derivatives with respect to x, y, and z.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

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: If f(x, y, z) = 16xy – 4yz – 4zx + 3, then the first order partial derivative fz = - - (4y + 4x) - –…

A: When a function is differentiated concerning a particular variable and the rest all the variables…

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: Let f(x, y) = ( 0, 0 < y < x 2 1, otherwise Verify the existence of partial derivatives fx(0, 0) and…

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Q: Find the first partial derivatives of the function. f(x, y, z, t) = 7xyz6 tan(yt) fx(x, y, z, t) =…

A: Given: The function f(x,y,z,t)=7xyz6 tanyt. To find: The first partial derivatives, fx(x,y,z,t)=…

Q: Find the first partial derivatives with respect to x, y, and z. 7xz w x +y aw %3D

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Q: Differentiate implicitly to find the first partial derivatives of z. x In(y) + y²z + z² = 27 Əz Əx…

A: Differentiate above equation with respect to x and y respectively.

Q: Find partial derivatives of  hxx ( x,y) , hxy(x,y), hyy (x,y)  For function  h(x,y)= ln ( x^3 +…

A: Given, h(x,y)=ln(x3+y3)

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: For the function f(x, y) = Vx³ + y³ find both partial derivatives at the point (0,0) (separate by…

A: Given function, f(x,y)=x3+y33

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

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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: ih fcuv, w) and its partial derivatives v and w with respecttou and and are Continows that u-x-y, V=…

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Q: Find the first partial derivative of fx , fy and fz of f ( x , y, z ) = 2xyz +  tan x  +  y sin z…

A: Given problem:- Find the first partial derivative of fx , fy and fz of f ( x , y, z ) = 2xyz + tan x…

Q: Find the first partial derivatives with respect to x, y, and z. fx, у, 2) %3 4x?у - 2хуz + бу2?…

A: Given  f(x, y, z) = 4x2y - 2xyz + 6yz2

Q: Use the limit definition of partial derivatives to find fx(x, y) and                    fy(x, y).…

A: Partial derivative:

Q: w = xy +z+ sin(x + yz)

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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: A function f has continuous second partial derivatives on an open region containing the critical…

A: Given: A function f has continuous second partial derivatives on an open region containing the…

Q: Use the chain rule to find the partial derivatives for and av z = coS x siny , x =u – v , y = u²…

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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: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4xy - 9xyz + 10yz2…

A: Given that, The function is following, f(x, y, z) = 4x2y - 9xyz + 10yz2 We have to find partial…

Q: Find the value of at the point (1, 1, 1) if the equation xy+ z°x – 2yz = 0 defines z as a function…

A: Given equation, xy+z3x-2yz=0

Q: ih fcuv,w) and its partial derivatives with respect tou and v and w and are Continous that usx-, V=…

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Q: ihe fcu,v, w) and its partial derivatives with respect tou and vand w and are Continous that u-メ-ツ…

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Q: Suppose that the partial derivatives of a function f(x.y.z) at point on the helix x=cost, y=sint,…

A: In this question, we have given the helix and first derivatives of f. x=cost, y=sint, and z=t and…

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

A: As we know that f=f(x,y,z)then fx(x,y,z)=∂f(x,y,z)∂x, fy(x,y,z)=∂f(x,y,z)∂y,  fz(x,y,z)=∂f(x,y,z)∂z

Q: Use the limit definition of partial derivatives to compute the partial derivative of the function…

A: The given function is f(x,y)=2-4x+2y-2x2y at a point (1,3)

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

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Q: Find the 1st order partial derivative of f(x,y,z) = 4x^3y^2 - e^zy^4 + (z^3/x^2) + 4y - x^16

A: The given function is f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16.

Q: Show that following function xY (x, y) + (0, 0), f(x, y) = x² + y² (x, y) = (0,0) is continuous,…

A: To check the continuity of given function at origin firstly finding the limit of the function at…

Q: Use the limit definition of partial derivatives to compute the partial derivative of the function…

A: We will find the partial derivative as following .

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: Differentiate implicitly to find the first partial derivatives of z. x + sin(y + z) = 0 az Əx az dy…

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Q: Find the first partial derivatives of the function. f(x, y, z) = x7yz2+ 4yz

A: From the given problem:   fx,y,z=x7yz2+4yz   So,   fxx,y,z=∂f∂x=∂ ∂ xx7yz2+4yz=∂ ∂ xx7yz2+∂ ∂…

Q: Differentiate implicitly to find the first partial derivatives of z. 2x? + 5y2 + 11z² = 81 %3D az ax…

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Q: Find the first partial derivatives of the function. F(x, y, z) = x³yz? + 8yz f,(x, y, z) = fy(x, y,…

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Q: Find the first partial derivatives of the function. f(x, y, z, t) = 7xyz9 tan(yt) fx(x, y, z, t) =…

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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: Find the indicated partial derivatives of: 2х — 2у - f(x, y) = 2х + 2y at the point (x, y) = (1,3).…

A: partial derivative of a function f(x,y) is defined as : ∂f(x,y)∂x treating y as…

Q: Calculate the partial derivative f2(3,3,1), where f(x, y, z) = xyz. %3D

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

A: Given      f(x,y,z) = 2x²y - 4xyz + 6yz²

Q: Let f(x, y) be a function whose partial derivatives exist and are continuous at a point (a, b).…

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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: Find the first partial derivatives of 2х — 4у - f(x, y) = at the point (x, y) = (2,2). 2х + 4y af…

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Q: Calculate the partial derivative f(5, 2, 5), where f (x, y, z) = xyz.

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Q: Find the first partial derivatives of the function. f{x, y, z) = x³yz² + 5yz f,(X, Y, 2) = Fy(x, Y,…

A: Here the given function is f(x, y, z)=x5yz2+5yz. We have to find the first partial derivatives fx(x,…