(3) Consider the derivative dz = 2xydx + (x² + 2y)dy Evaluate whether this is a total derivative, by integrating along straight lines (i) (x1, y1) → (x2, Y1) then (x2, y1) → (xX2, Y2); and (ii) (x1,Y1) → (X1, Y2) then (x1, y2) → (x2, Y2).

Q: find the gradient of the function and the maximum value of th directional derivative at the given…

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Q: Calculate the partial derivative of the function f(x, y, z) = xyz at the point (0, 1, 1).

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

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

A: According to our policy at Bartleby, I can solve only 1 question. Given a function : g(x,y)=12x+5y2…

Q: Use the Chain Rule to evaluate the partial derivative at the point (u, v) = (0,5), where g(x, y) = x…

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Q: dz at the point (1,1,1) if the equation 4xy +z°x-2yz = 3 defines z as a function of the two…

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Q: Find the first partial derivatives of the function. 4x – 7y f(x, y) = %3D 4x + 7y A(x, y) = Wx, y) =

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Q: Find the value of 0z/0x at the point (1, 1, 1) if the equation xy + z3x - 2yz = 0 defines z as a…

A: Given, the equation is xy + z3x – 2yz = 0 and defines z as a function of the two independent…

Q: find the total derivative of z = f(x,y) = 2x+xy-y2 where x=g(y)=3y2

A: Given function: z=2x+xy-y2 where x=3y2 Putting the value of x in z , we get…

Q: Find the second partial derivative of the function f(z, y, z) = 2°yz+ at the point (1, 1, 1). yz

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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 partial derivative of f (x, y) = e2+3y cos (x³y²) with respect to x. O fa (x, y) = e2x+3y…

A: Given f(x,y)=e2x+3ycosx3y2 To differentiate f(x,y) partially with respect to x Let u=e2x+3y…

Q: Find the value of ∂z/∂x at the point (1, 1, 1) if the equation xy + z3x - 2yz = 0 defines z as a…

A: Given, the equation xy + z3x – 2yz = 0, defines z as a function of two independent variables x and y…

Q: Find the partial derivative of f(x, y) 8x - 2xy2 + y3 with respect to x at the point (2, 1, 61).

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Q: Find the derivative of the function at P, in the direction of A 1) f(x, y) = 2xy – 3y², P,(5,5), A=…

A: We have given function, we have to find directional derivative.

Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz ,at the point P. (0,0,0) in the…

A: We have a given function g=3e^x cos(yz)

Q: Find the derivative of the function at P, in the direction of A 1) f(x, y) = 2xy – 3y², P,(5,5), A=…

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Q: Find the partial derivative. (2² + 4x – 4y)* z = dz

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Q: Find the partial derivative at point(u,v)=(-4,0) of w=ln(xa+yb+za),x=uevsin u y=uevcos u, z=uev,…

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Q: (a) Find the partial derivative of f with respect to x. fx(X, y) = (b) Find the partial derivative…

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Q: Find the value of ∂x/∂z at the point (1, -1, -3) if the equation xz + y ln x - x2 + 4 = 0 defines x…

A: Given equation is xz+ylnx-x2+4=0. Given point is 1,-1,-3. Partial derivative of given equation with…

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

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Q: of ) Find the first order partial derivative of and for the function f (x, y) = x/y -x²y+y² ây

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Q: 8. Find the directional derivative of f (x, y, z) = xyz3 at P(2, 1, 1) in the direction of Q(0,…

A: Ans=1 I have considered image question bcz I think you have done mistake while typing... Now go…

Q: If f(x, y) = y cos(x) – a° In(y), find the second partial derivative ду дх .A 3x2 = -2y sin(x) ду дх…

A: Option (a) is correct.

Q: Get the first order derivative of the function x + sin(y – 2x) - 1= 0 - 2 1 a. y' = cos(y-2x) 1 b.…

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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: Compute the partial derivative of the function f(x, y, z) = e'-z cos(y) +ze-/(1+y²) with respect to…

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Q: f(x,y)=ln(5x+4y). Find the directional derivative of f at (1,0) in the direction of the line…

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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: A function x x(y, z) is defined implicitly by the equation 2 x4 + 2 y4 +3 x y z+z² = 0 Use implicit…

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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: 2. Find the derivative of f(x, y, z) = x³ - xy2 - z at Po(1,1,0) in the direction of V = 2ỉ – 3j +…

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Q: 2 - What is the directional derivative of the function f(x,y,z) = x3 - 2xy +z at point Ao= (1,1,0)…

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Q: f (x, y) = 3x^3 −9x+9xy^2. Use the second derivative test to classify the critical point (1,0) as a…

A: Recall: second derivative test : (i)  Firstly find critical points . i.e, fx(x,y) =0 and…

Q: The second order partial derivative of f with respect to z (mean fz) where f(x, y, z) = x'0 sin(3y +…

A: Given: fx,y,z=x10 sin3y+10z To determine: fzz

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: b) Use the chain rule for partial derivative to find 2 when z = f(x, y) = x²y + ln(x + y) and (x, y)…

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Q: Find both first partial derivative h(x, y) = e-(xª + y^) hx(x, y) = hy(x, y)

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Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 7y + 3z) at the point (– 2, – 3, – 6). - -

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Q: 8. Find the directional derivative of f (x, y, z) = xy²z³ at P(2,1,1) in the direction of Q(0, –3,5)

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

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Q: Find the derivative of f at point P in the direction of u. f(x, Y, 2) = 9a² + 2y² – 72², P = (6,7,…

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Q: 5. Find the second partial derivatives of f(x, y) = x²y³ + 3y?

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Q: Find the partial derivative of u = x^2 + y^2 + z^2 - 4xyz

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

A: The given function is f(x, y, z) = 3x2y − 5xyz + 10yz2

Q: Find the first partial derivatives of 3x – 2y f(x, y) = at the point (x, y) = (1,4). 3x + 2y af…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Find both first partial derivatives. f(x, y) = 3x - 9y + 8 F,(x, y) f,lx, y) = |

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Q: Find all the first partial derivatives of; glw,2, y, z) = xe2w - wyz?

A: Topic:- partial derivatives