Find fa, fy, and fz. f (x, y, z) = z In(xʻy° cos(52)) 4,3 COS x*Y fn = fy = fz =

Q: Q1// B: If u+v=e cos y and u-v=e'sin yfind the Jacobain of the a u, v at (x.y) (1,0) dx,y function

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Q: Find Oz/ou and oz/ov for z=4e* ln(y), x=ln(u cos(v)), y = usin(v) at the point (u, v)=(2.7/4).

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Q: dz dt Consider x = cos t, y = sint and z = x2 +y². Then ulan ||

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Q: dz Find when u= 0, v= 1 if z= sin(xy) + ysin(x), x = uv, y3Du² +v?. du

A: Given  z = sin(xy) +ysin(x)              x = uv and y = u2 + v2  Substituting x and y in z we have…

Q: dw Use the Chain Rule to find where w = cos 8x sin 2y, x = and y = t*. dt 4' dw II

A: w=cos8x sin2y  , x=t4 and y=t4 dxdt=dt4dt=14 dydt=dt4dt=4t3   ∂w∂x=8 cos8x cos2y ∂w∂y=sin8x -2 sin2y…

Q: Find Oz! ôu and dzlôv for z= 4e" In(y), x In(u cos(v), y=u sin(v) at the point (u,v)= (2, 7 / 4).…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: (a) z = x2 + y² + xy, x = sin t, y = e'. (b) z = x2 + y², x = cos t + sin t, y = cost – sin t. %3D

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Q: f(r,t) = cos(3r) exp(4t) %3D fi(x,t)+ frz(x,t) = f(r,t) %3D

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Q: 2n X f(p sin()cos(0) p sin ()sin(e) • p cos(o) p'sin (4) f(x, y, z) dV = dp de de Jn/2

A: SPHERICAL COORDINATES : The spherical coordinates are : x=ρsin θcosϕy=ρsin θ sinϕz=ρcosθJ=ρ2sinθ…

Q: Let v(x, y) = cos(4x)sinh(4y). Find f(z)with Im(f(z)) = v(x, y). I

A: Given function is v(x,y)

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A: We have given fx,y,z=tanhx+2y+3z and we have to calculate fx,fy and fz

Q: Let w = x2e2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y =…

A: Given: w=x2e2ycos3z x=cost y=lnt+2 Putting x, y and z in w, we get…

Q: Let w = x^2e^2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y…

A: Given  By chain rule of differentiation , we have

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Q: f(x,y,z)= (x+1)cos(x² + yz); find ôxôyôz at (0,1,7). el1+:) g(x, y, z)= find 8 zyy ,1,0 sin(x+z)'

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Q: dz Find when u= 1, v=0 if z= cos(xy) – xsin(y), x= u² + v2, y= uv. dv A) 2 B -1 D) 1 E -2

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Q: The equations xcos(u) + 9uy2 + e² + 2 = 0 and 3ye" + 4x²v – 3æcos(2) +1 = 0 are solved for u and v…

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Q: Find fa, fy, and fz. f (x, y, z) = 3z In (x°y³ cos(4z)) fr = %3D fy = fz =

A: Given that , fx,y,z=3zlnx6y3cos4z find fx , fy and fz.

Q: (+ > 0, => 0). -tz г () dt t=0 Know that (*) is true also for s > 0, and (- > , z = x e'y = x cos y…

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Q: S[[ 2xdV where E = {x, y, z) |0 < y < 2,0 sxs4-y²,0<= <y} E [[[ vz cos(x* kiV where E = {x, y, z)…

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Q: ZX = 24, XY = 10, and YZ 26. Find cos Y. %3D 5/12

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Q: х. у 2) w=¨+2,x= cos“(t), y = sin°(1), z =-, at t = 3 Z Z t

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Q: uxx+uyy=0; u1(x,y)=cos x cosh y, u2(x,y)=ln(x2+y2)

A: Given:

Q: 3. Let z = x?y + 3xy+ where x = sin 2f and y cos t. Use the chain rule to dz find when t = 0. dt

A: As indicated in the question, we will make use of chain rule of differentiation. Recall that the…

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Q: 3- h(x, y, z) = cos xy + e*y + In zx, Po (1,0,1/2), A = i + 2j + 2k

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Q: В. Find dz/dx , əz/@y at the point (1,1,1) if x³ + z2 + ye*z + xz cos y = 0 .

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Q: Let f(x, y, z) = ln(x² + z) + y²e#z – cos(2yz). Find fzya.

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Q: Let v(x, y) = cos(4x) sinh(4y). Find f(z)with Im(f(z)) =v(x, y).

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Q: Find the potential P(x,y) attached to the exact ODE 2x sin(y) +x² cos(y) y' = 0

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Q: 5 Qu/ If w=f(u, v) = cos uv, u = xyz , v = 4(x²+y²) dw Prove that 0 at the this point…

A: Given problem:-

Q: Let w = x°e4y cos(9z). Find the value of dwldt at the point (3, ln 5, 0) on the curve x = 3 cos(t),…

A: Given: w=x6e4ycos(9z)x=3 cos(t)y=ln(t+5)z=6tDifferentiating we…

Q: Let v(x, y) = cos(4x)sinh(4y). Find f(z)with Im(f(z)) = v(x, y).

A: using CR equation we get....

Q: Q.5) Evalute ar F. ar ds dy R where F(x, y, x) = 2k and r(x, y) = sinx cosy i+ sinx sinyj+ cosx k.

A: To evaluate: The integral ∬R F.∂r∂x×∂r∂yds where F(x, y, z)=2k→ and r(x, y)=sinx cosy i→ + sinx siny…

Q: Find fa, fy, and fz. f(x, y, z) = 5z ln(x³y³ cos(z)) fx = fy fz f₂ = =

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Q: 3) Find if w = 5 cos(xy) – sin(xy), x = ,y = t,z = t³ %3D dt

A: Let's find.

Q: Find fr, fy, and fz. f (x, y, 2) = z In(x*y³ cos(52)) 4.3 fa = fy = fz =

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Q: Compute cos(x) cos(y) dx – sin(x) sin(y) dy, where c(t) = (9t, t2), 0 sts 1. (Round your answer to…

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Q: (g) f (x,y,z) = x² + y? – 2z? + zlnx in P(1,1,1) (h) f(x,y, z) = e*+Ycosz + (y + 1) sin -1x in…

A: Gradient is a vector quantity that represents the rate by which function value is changing. Gradient…

Q: h of the DE's =)y = 2 sin² x ; y(0) = 0 , y'(0) =-2

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Q: 1. Let z = f(x, y), find for: and dy - - (a) e"y + z ln y = 0 (b) yz – sin z = xy

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 6 cos x – sin xy; Y = 8t %3D t' Enter…

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Q: 4. Find дw b. dz a. дх at the point (x, y, z) = (0, 1, T) if w = x² + y? + z? and y sin z + z sin x…

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Q: Calculate dz/du and dz/dv given the following functions: 2x-y x + 3y' = f(x, y) = = Z = x(u, v) =…

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Q: E(z, t) = ex cos(@t – kz + Þ1) + ey cos(wt – kz + $2) = €;E× +e,Ey %3D

A: Consider the given equation: Where,

Q: 3. Let V = eP cos(qr), with p = x In(xyz), q = z cos(Ty) and r = 2 tan-(y). %3D By using the chain…

A: Solve the given problem.

Q: Find fa, fy, and fz. f(x, y, z) = 3z ln (x³y³ cos(2z)) fx= fy= f₂ = =

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Q: 1 COS Z dz, C : |2| = 3z Integrate counterclockwise 9. COS Z dz 3z

A: We have to find Given Complex integral using Cauchy Residue Theorem.