Given f(u, v), where u = x² y, v = xy? If at the point (2,3), f, = 4, fm = 3, fm = 5, ƒ, = 1, fm =6. Find fm at p(2,3)

Q: Given f(x, y) = x² – 3x?y – y", find fz(r, y) = fy(x, y) = frz(x, y) = fzy(x, y) =|

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Q: Find ôf af of and дх ду dz f(x, y, z) = 3×EYZ + 7yexz af -7 Əx af 7 ду af 3xe"y + 7yex %3D X ze

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Q: Given f(x, y, z) = 3x – 2y + 1z, find f. (æ, y, z) = fy(x, y, z) = f:(x, y, z) = |

A: We are given with the function f(x,y,z) and need to find the derivative fx,fy and fz.

Q: Given f(z, y) = – 3z' + ry° + 5y², find fr(x, y) = | fy(z, y) = |

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Q: if z=xarctan(y/z), find ∂z/∂x at x=0, y=1, z=1

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Q: Suppose f(x, y) = x" + y*. Find fa(1, 1), f,(1, 1), and fz (x, y)

A: Given :f(x,y)=xy+yx

Q: Calculate ∬Sf(x,y,z)dS For x^2+y^2=9,0≤z≤3;f(x,y,z)=e^(−z) ∬Sf(x,y,z)dS= ?

A: Find the parametric equation for the given curves.

Q: if f(x,y)= ln(x^2 +y^2), find fxx(x,y) + fyy(x,y)

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Q: If f(x, y) = 3x – 7y, r(t) = (tª, t³), t= 2, then what is 4 f(r(t)) att = 2? dt

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Q: If f(x,y,z) = e2x+3y-4z + xyz And x = 3si n(rt) y = 2cos(rt) z = r² + t² af Find at

A: Given that,  fx,y,z=e2x+3y-4z+xyz And  x=3sinrty=2cosrtz=r2+t2 If F=fx,y,z, Where, x, y, z are…

Q: Utt = Uxx, x>0, t > 0, u(x,0) = f(x), u₁(x,0) = 0, u₂(0,t) = 0, where f(x) = { b) Sketch the…

A: solutions are given below:

Q: If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z – x, show that fe af af + = 0.…

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Q: now if we take F (x, y) = (ax, ay), where a is any positive constan %3D

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Q: Given f(x, y) 1* + 2xy° + 4y“, find fz(T, y) = fry(1, y) =

A: The given function is f(x,y)=-x3+2xy6+4y4

Q: Given f(x, y, z) = x³yz². Find f.(1,1,1).

A: The equation we have , f(x,y,z) = x3yz2 We have to find out fz, Now we differentiate f(x,y,z) with…

Q: If f(x, y) = (xy)", with |xy| < 1, find 2 af af and n=0 fe -y/(1-xy)^2 af -x/(1-xy)^2 dy

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Q: Find fz(x,y) and fy(x, y) given f(r, y) = csc yArcsin(r²).

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Q: 1 If (x, y)= find f, and f,. Vx? x²+y²

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Q: If f(x, y) = 8xey + 8y Inx, then is given by:

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Q: ) and f(x) = u(x, y) + iv(x, y) is analytic, %3D

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Q: Given f(x, y, z) = V 4a? + 2y? + z², find fz(x, y, z) = fy(x, y, z) = f:(x, y, z) = |

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Q: f (z,y, z) = x² + y² + 2² subject to zyz = 4

A: Given: fx,y,z=x2+y2+z2 subject to xyz=4 Let gx,y,z=xyz-4 Using Lagrange Multiplier fx=λgx, fy=λgy,…

Q: Given f(x,y,z)=√(−6x+5y+2z), find fx(x,y,z) = fy(x,y,z) = fz(x,y,z)=

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Q: Given f(2, y, z) =v V-I - 2y + z, find f.(z, y, z) = f(z, y, z) = f(1, y, z) =

A: We will use definition of differentiation. First we will handle derivative of the root of the…

Q: f(x, y, z) = 3x + 2y + 4z, x2 + 2y2 + 6z2 = 21

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Q: If f =x-e" and F=x'yi-2y'zj + xy'z'k, find: div(F x grad(yf )) at (4,1,-2)

A: The function                     Then, we have to find

Q: Given that f(r, v) = xain v, determine fy(z, y).

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Q: Given the function f(x,y)=e5-2x+3y, approximate f(4.1,0.9)using point (4,1) for (xo, yo). What is…

A: The linear approximation of f(x, y) at (a, b) is the linear function  L(x, y)=f(a, b)+fx(a,…

Q: If f(x, y, z) = xy + z?x - 3yx z?, find fxy ?

A: If fx,y,z=xy+z2x-3yx2z2 Find fxy ?

Q: 10. If z = x + f(u), where u = xy, show that дz dz х дх = x. ду

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Q: Given f(x,y,z) = x³yz². Find fy(1,1,1)

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Q: Find Duf at P. 1 2. f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u %3D - -

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Q: If = 2 z-x'y and A = 2x'î-3 yzj +x z'k, find A.V and A xV4 at the point ( 1,-1,1).

A: given ϕ=2z-x3y and A=2xi^-3yzj^+z2 k^ find at the point 1,-1,1 1) A·∇ϕ 2) A×∇ϕ

Q: If F (x, y, z) = xyzî – e² cos xĵ + xy² z³k, what is V · (V×F) (1, 2, 3) 1 2

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Q: Given f(æ, y) = e"" Y' – z°y", show that fæy = fyæ.

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Q: Given f(x, y) = 3x° cos (y"), find f-(r, y) = fy(x, y) = fae (x, y) = fyz (x, y) =

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Q: Suppose Vf(x, y, z) = 2xyzexi + zex¯j + yex k. If f(0, 0, 0) = 1, find f(1, 3, 3). ,2 .2

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Q: Suppose Vf(x, y, z) = 2xyze*i + ze*j + ye* k. If f(0, 0, 0) = 1, find f(3, 1, 3).

A: follow next step

Q: Find f,, fy, and f, for f(x,y,z)= 5xy+ 3xz + yz.

A: It is partial derivative

Q: Given f(r, y) 2x* + 4x²y² – 5y°, find fz(x, y) - fy(x, y) = fzz(T, y) = fzy(T, y) =

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: Let f (x, y, z) = xy + z. Calculate - df/ds, where as x=s2 , y=st, z=t2

A: Given f(x,y,z) =xy+z , x=s2 , y=st and z=t2. We need to calculate -df/ds.

Q: Given f(x, y, z) = x³yz². Find fy(1,1, 1).

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Q: Given f(x, y, z) = V5x – 5y + 2z, find fa(x, y, z) =| %3D fy(x, y, z) = f-(x, y, z) =|

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Q: xyz f(x.y.z) = et ot function is given P(2,,4) in point fux + fyy + fzz colculate.

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Q: Given that f(r, y) = }2 - - . (a) Calculate: f,, (b) Calculate: f„, (c) Are they equal?

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Q: Let f(x, y) = 4x + 3y and let 7 (t) be the line segment from (1, 1) to (–2, 5). Then 7 (t) =…

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Q: Given: f (x, y, z) = 2x'yz² + 5x°y*z® - x³y? ,5_3 Required: fzyx , fxzz

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Q: Find Vf(x, y) if f(x,y) = e** cos y ..... ...

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Q: Use the linear approximation to ƒ(x, y) 12x² at (3, 9) to estimate f(3.1, 8.8). y2+7 (Use decimal…

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