4) Find f, fy and f, for the following i) f(x,y,z) = sin-xyz ii) f(x, y,z) = y z In xy iii) f(x,y,z) = e-xyz

Q: dx 1)y /sec(3x) 2) y = Vu + 2u , x= u? - 3u

A: Definition used -            Chain rule of derivative -                             ddx(f(g(x))=…

Q: If f (x, y, z) = x'y° z2 + 2°x°y, then fyrzz: (-1, 1, 1) %3D yZI ZIZ

A: Given function is fx,y,z=x3y3z2+z3x3y. We have to find the fyzxzxz−1,1,1. First differentiate…

Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

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

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Q: For the linear operator L = D^2 −4D + 8, determine L(y) for y = e^(2t), y = e^(2t)sin(2t), and y =…

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Q: Find a function that satisfies the conditions f " (x)=x8, f'(0) = 13, f(0) = 10.

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Q: af dy of f(x, y) = tan (x²y³ + 2xy)? What is the

A: Given:     To determine:

Q: Let f(z, y) — (-(г + ))5. Then | 20(-(x+y))^3 dzðy dzðydz dz²dy

A:

Q: Let sin(4x + 7y°) x3 + y5 if (x, y) # (0,0) f(x, y) = 0. if (x, y) = (0,0) %3D Which of the…

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Q: Q.2 Differentiate the function y = 2x - 3x + 4 2) y = xcosx 3) y (1 + x2)3 sinx 4) y = 5) y = tan x…

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Q: If F(x,y,z)=sin(x³y²)+cos (Vxy2)+x®y²z, then fyz(1,-2,1)=

A:

Q: Determine the two-variable function F(x, y) if Fy (x, y) = y sin(xy) + x given that x^2 + πχ2 F(x₁ -…

A: Given That: Partial derivative of a function with respect to y is Fy(x,y)=ysin(πxy)+x with the…

Q: a3 f 2- Find the third derivative for for f (x, y) = sin əx3 -2sin?cos()+2 sin) sin By'sini )+2…

A: The given function isf(x, y)=sinxy

Q: f(x, y, z)= 1+ 2xy³+3y- Find the following: a) fz(x, y, z) b) f(1,1,1) c) fz(x, y, z) d) f.(1, 1, 1)

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

Q: iv is analytic = -11..

A:

Q: Let h(æ, y) = f(x)g(y) + (9(y))² and suppose that f(1) = 5, f'(1) = 3, g(2) = 8, g'(2) = 10. Then…

A: Given function is - h(x,y) = f(x) g(y) + g(y)2             ............................(1)We have to…

Q: Let F(2) = f(x) and G(x) = (f(x)) - You also know that a = 2, f(a) = 2, f'(a) = 7, f'(a³) = 15. Find…

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Q: If f(x.y,z)= y + xz then f ,(1,1,1) =

A: The given function is  f(x, y, z) = y5 + xz

Q: 12. Find frxyz for f (x, y, z) = sin (3x + yz)

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Q: af If f(x,y) = sin-(4x³y?) then dx 12x?y? 1-(4x³y²)² O a. b. 1 4x³y²/(4x³y?)² – 1 c. 12x²y² 4x³y?…

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Q: 2. At what points of R² is the function continuous? (sin(x² + y²) x² + y² f(x, y) = 0, -, if (x, y)…

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Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4).…

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Q: 3 For f(x,y) = In x+y°, 4,8)

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Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

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Q: Let f(1,y) = (r+ay°,r²y°,2r + by), g(u, v,w) = (3u² + bv² + w°, uvw). Find the derivative of…

A: Let f(x, y)=x3+ay2, x2y3, 2x+by,  gu, v, w=3u2+bv2+w3, uvw. We need to find the derivative of fgu,…

Q: 2. (5) Find f, for the function f(x, y) = sin (x + y²)

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Q: e) s = cos (1– 21) -2 4t f) y = t+1, .2 x + x g) y =

A: